Mathematics, 23.08.2019 08:00 deonte4807

Using the quadratic formula to solve 4x2-3x+9 = 2x+1 what are the values of x?

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Answer from: ciel8809

we know that

The formula to calculate the solutions of the quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}$

in this problem we have

$4x^{2}-3x+9=2x+1$

$4x^{2}-3x+9-2x-1=0$

$4x^{2}-5x+8=0$

$a=4\ b=-5\ c=8$

substitute in the formula

$x=\frac{-(-5)(+/-)\sqrt{(-5)^{2}-4(4)(8)}}{2*4}$

$x=\frac{5(+/-)\sqrt{25-128}}{8}$

$x=\frac{5(+/-)\sqrt{-103}}{8}$

remember that

$i=\sqrt{-1}$

$x=\frac{5(+/-)i\sqrt{103}}{8}$

therefore

the answer is

the solutions are

$x=\frac{5+i\sqrt{103}}{8}$

$x=\frac{5-i\sqrt{103}}{8}$

Answer from: bglosson4333

The value of which satisfies the given quadratic equation are $\fbox{\begin\\\ \math x_{1}&=\dfrac{5+ i\sqrt{103}}{8} \ \ x_{2}&=\dfrac{5- i\sqrt{103}}{8}\\\end{minispace}}$

Further explanation:

The given equation is $4x^{2}-3x+9=2x+1$

From the given equation it is observed that the degree or the highest power of the variable is .

This implies that the given equation is a quadratic equation.

A quadratic equation is an equation whose degree or the highest power of the variable is .

To obtain the solutions of the given quadratic equation express the given equation in its simplest form i.e. collect all the variables on the left side of the equation.

$\begin{aligned}4x^{2}-3x+9&=2x+1\\4x^{2}-5x+8&=0\end{aligned}$

The above equation is a quadratic equation with its leading coefficient as .

Since, the degree of a quadratic equation is so, the there are two roots of the given quadratic equation.

The solutions of a quadratic equation are the points where the curve of the function intersects the -axis.

The solution of a quadratic equation of the form $ax^{2}+bx+c=0$ is calculated as follows:

$\fbox{\begin\\\ \math x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}\\\end{minispace}}$

The above formula is called the quadratic formula.

On comparing the quadratic equation $4x^{2}-5x+8=0$ with the general form of the quadratic equation it is observed that the value of is , value of is and the value of is .

To obtain the solution of the given quadratic equation substitute the value of $a,b\ \text{and}\ c$ in the quadratic formula.

$\math x&=\dfrac{-(-5)\pm\sqrt{(-5)^{2}-4\times4\times8}}{2\times4}\\x&=\dfrac{5\pm\sqrt{25-128}}{8}\\x&=\dfrac{5\pm\sqrt{-103}}{8}\\x&=\dfrac{5\pm i\sqrt{103}}{8}$

In the above equation $i=\sqrt{-1}$

The first value of is as follows:

$\fbox{\begin\\\ \math x_{1}=\dfrac{5+ i\sqrt{103}}{8}\\\end{minispace}}$

The second value of is as follows:

$\fbox{\begin\\\ \math x_{2}=\dfrac{5- i\sqrt{103}}{8}\\\end{minispace}}$

Therefore, the two values of which satisfies the given quadratic function are as follows:

$\fbox{\begin\\\ \math x_{1}&=\dfrac{5+ i\sqrt{103}}{8} \ \ x_{2}&=\dfrac{5- i\sqrt{103}}{8}\\\end{minispace}}$

Learn more:

1.A problem on composite function link

2.A problem to find radius and center of circle link

3.A problem to determine intercepts of a line link

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Quadratic equation

Keywords: Quadratic, expression, equation, quadratic equation, solution, roots, highest power, degree, variables, leading coefficients, quadratic formula, x-axis, formula, general form.

Answer from: Quest

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction: this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology: the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion: the last is the discussion, this can be either by management people or persons who are all interested , etc.

Answer from: Quest

300b(x) is graphed by the functio

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