Which value for x makes the open sentence true? 7 + 6 • x = 42 + x2

The possible values of x are 3±√26i

Step-by-step explanation:

Given the equation, 7 + 6x = 42 +x², to find the value of x that makes the expression true, we need to rearrange the expression and factorize the resulting equation.

Rearranging:

7 + 6x = 42 +x²

Moving 7+6x to the other side we have:

x²+42-6x-7 = 0

x²-6x+35 =0.

Using the general formula

x = -b±√b²-4ac/2a

From the quadratic function, a = 1, b= -6, c=35

x = 6±√(-6)²-4(1)(35)/2(1)

x = 6±√36-140/2

x = 6±√-104/2

x = (6±√104×-1)/2

x = 6±√104i/2

x = 6±2√26i/2

x = 3±√26i

Note that √-1 = I (a complex value)

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