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Simplifying (12 + -2x)(16 + -2x) = 56x Multiply (12 + -2x) * (16 + -2x) (12(16 + -2x) + -2x * (16 + -2x)) = 56x ((16 * 12 + -2x * 12) + -2x * (16 + -2x)) = 56x ((192 + -24x) + -2x * (16 + -2x)) = 56x (192 + -24x + (16 * -2x + -2x * -2x)) = 56x (192 + -24x + (-32x + 4x2)) = 56x Combine like terms: -24x + -32x = -56x (192 + -56x + 4x2) = 56x Solving 192 + -56x + 4x2 = 56x Solving for variable 'x'. Reorder the terms: 192 + -56x + -56x + 4x2 = 56x + -56x Combine like terms: -56x + -56x = -112x 192 + -112x + 4x2 = 56x + -56x Combine like terms: 56x + -56x = 0 192 + -112x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(48 + -28x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(48 + -28x + x2)' equal to zero and attempt to solve: Simplifying 48 + -28x + x2 = 0 Solving 48 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -28x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + -28x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -28x + x2 = 0 + -48 -28x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -28x + x2 = -48 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -48 + 196 Reorder the terms: 196 + -28x + x2 = -48 + 196 Combine like terms: -48 + 196 = 148 196 + -28x + x2 = 148 Factor a perfect square on the left side: (x + -14)(x + -14) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (x + -14) equal to 12.165525061 and -12.165525061.Subproblem 1
x + -14 = 12.165525061 Simplifying x + -14 = 12.165525061 Reorder the terms: -14 + x = 12.165525061 Solving -14 + x = 12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 12.165525061 + 14 Combine like terms: -14 + 14 = 0 0 + x = 12.165525061 + 14 x = 12.165525061 + 14 Combine like terms: 12.165525061 + 14 = 26.165525061 x = 26.165525061 Simplifying x = 26.165525061Subproblem 2
x + -14 = -12.165525061 Simplifying x + -14 = -12.165525061 Reorder the terms: -14 + x = -12.165525061 Solving -14 + x = -12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -12.165525061 + 14 Combine like terms: -14 + 14 = 0 0 + x = -12.165525061 + 14 x = -12.165525061 + 14 Combine like terms: -12.165525061 + 14 = 1.834474939 x = 1.834474939 Simplifying x = 1.834474939Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.165525061, 1.834474939}Solution
x = {26.165525061, 1.834474939}
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