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x² + 20x + 100 = 36⇒ x² + 20x + 100 - 36 = 0⇒ x² + 20x + 64 =0

Δ = b²-4ac = 20² -4·1·64 = 400-256 = 144

x₁= (-b+√Δ)/2a = (-20+√144)/2·1 = (-20+12)/2 = -8/2 = -4
x₂= (-b-√Δ)/2a = (-20-√144)/2·1 = (-20-12)/2 = -32/2 = -16

x=-4 or x=-16

The solution to the quadratic equation x² + 20x + 100 = 36 is x = 4 or x = -16 option (a) is correct.

What is a quadratic equation?

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]

We have an quadratic equation:

x² + 20x + 100 = 36

[tex]\rm x^2+20x+64=0[/tex]

a = 1, b = 20, and c = 64

[tex]\rm x_{1,\:2}=\dfrac{-20\pm \sqrt{20^2-4\cdot \:1\cdot \:64}}{2\cdot \:1}[/tex]

After solving:

x = 4 or x = -16

Thus, the solution to the quadratic equation x² + 20x + 100 = 36 is x = 4 or x = -16 option (a) is correct.

Learn more about quadratic equations here:

brainly.com/question/2263981

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