The values of the x are -6.59, and -9.42 if the quadratic equation is (x + 8)² - 2 = 0.
Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
The complete question is:
Solve for x.
Enter the solutions from least to greatest. Round to two decimal places.
(x + 8)² - 2 = 0
It is given:
(x + 8)² - 2 = 0
Using (a + b)² = a² + 2ab + b²
x² + 16x + 64 - 2 = 0
x² + 16x + 62 = 0
Compare with the standard form of the equation:
a = 1
b = 16
c = 62
Plug the above values in the formula:
[tex]\rm x = \dfrac{-16 \pm\sqrt{16^2-4(1)(62)}}{2(1)}[/tex]
x = [-16 ±√8]/2
x = [-16 ±2.83]/2
Take + sign:
x = [-16 + 2.83]/2
x = -6.59
Take - sign:
x = [-16 - 2.83]/2
x = -9.42
Thus, the values of the x are -9.42, and -6.59 if the quadratic equation is (x + 8)² - 2 = 0.
Learn more about quadratic equations here:
brainly.com/question/2263981
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