Solve for x, 2x² = 128

Solution:

Given: Equation is 2x² = 128.

Let us use the algebraic identity to solve the equation.

2x² = 128 can be expressed as 2x² - 128 = 0.

By taking out the common terms, we get

2 (x² - 64) = 0

x² - 64 = 0 [By using the zero product rule]

By using algebraic identity,

a² - b² = (a - b) (a + b)

(x)² - (8)² = (x - 8) (x + 8) = 0

Considering the two factors equal to zero, we get

x - 8 = 0 and x + 8 = 0

x = 8 and x = - 8.

Hence, the solution of the equation 2x² = 128 is x = 8 and -8.

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Solve for x, 2x² = 128

Summary:

The equation 2x² = 128 has two solutions x = 8, and - 8.