Use the discriminant to determine how many and what kind of solutions the quadratic equation x2−x=−14 has.

see explanation

Step-by-step explanation:

Given a quadratic equation in standard form : ax² + bx + c = 0 ( a ≠ 0 )

Then the discriminant Δ = b² - 4ac determines the type of solutions

• If b² - 4ac > 0 then roots are real and distinct

• If b² - 4ac = 0 then roots are real and equal

• If b² - 4ac < 0 then roots are not real

Given

x² - x = - 14 ( add 14 to both sides )

x² - x + 14 = 0 ← in standard form

with a = 1, b = - 1, c = 14

b² - 4ac

= (- 1)² - (4 × 1 × 14) = 1 - 56 = - 55

Since b² - 4ac < 0 then roots are not real

7.25

step-by-step explanation:

we know that 7 equals to 7.0. we also know that 1/4=0.25. so we can add the two together and we get 7.25

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.