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Simplifying (x + -12)(x + -12) = 8 Reorder the terms: (-12 + x)(x + -12) = 8 Reorder the terms: (-12 + x)(-12 + x) = 8 Multiply (-12 + x) * (-12 + x) (-12(-12 + x) + x(-12 + x)) = 8 ((-12 * -12 + x * -12) + x(-12 + x)) = 8 ((144 + -12x) + x(-12 + x)) = 8 (144 + -12x + (-12 * x + x * x)) = 8 (144 + -12x + (-12x + x2)) = 8 Combine like terms: -12x + -12x = -24x (144 + -24x + x2) = 8 Solving 144 + -24x + x2 = 8 Solving for variable 'x'. Reorder the terms: 144 + -8 + -24x + x2 = 8 + -8 Combine like terms: 144 + -8 = 136 136 + -24x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 136 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-136' to each side of the equation. 136 + -24x + -136 + x2 = 0 + -136 Reorder the terms: 136 + -136 + -24x + x2 = 0 + -136 Combine like terms: 136 + -136 = 0 0 + -24x + x2 = 0 + -136 -24x + x2 = 0 + -136 Combine like terms: 0 + -136 = -136 -24x + x2 = -136 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -136 + 144 Reorder the terms: 144 + -24x + x2 = -136 + 144 Combine like terms: -136 + 144 = 8 144 + -24x + x2 = 8 Factor a perfect square on the left side: (x + -12)(x + -12) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -12) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -12 = 2.828427125 Simplifying x + -12 = 2.828427125 Reorder the terms: -12 + x = 2.828427125 Solving -12 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 2.828427125 + 12 Combine like terms: -12 + 12 = 0 0 + x = 2.828427125 + 12 x = 2.828427125 + 12 Combine like terms: 2.828427125 + 12 = 14.828427125 x = 14.828427125 Simplifying x = 14.828427125Subproblem 2
x + -12 = -2.828427125 Simplifying x + -12 = -2.828427125 Reorder the terms: -12 + x = -2.828427125 Solving -12 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -2.828427125 + 12 Combine like terms: -12 + 12 = 0 0 + x = -2.828427125 + 12 x = -2.828427125 + 12 Combine like terms: -2.828427125 + 12 = 9.171572875 x = 9.171572875 Simplifying x = 9.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.828427125, 9.171572875}
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