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Simplifying (2x + -8)(2x + -8) = 3 Reorder the terms: (-8 + 2x)(2x + -8) = 3 Reorder the terms: (-8 + 2x)(-8 + 2x) = 3 Multiply (-8 + 2x) * (-8 + 2x) (-8(-8 + 2x) + 2x * (-8 + 2x)) = 3 ((-8 * -8 + 2x * -8) + 2x * (-8 + 2x)) = 3 ((64 + -16x) + 2x * (-8 + 2x)) = 3 (64 + -16x + (-8 * 2x + 2x * 2x)) = 3 (64 + -16x + (-16x + 4x2)) = 3 Combine like terms: -16x + -16x = -32x (64 + -32x + 4x2) = 3 Solving 64 + -32x + 4x2 = 3 Solving for variable 'x'. Reorder the terms: 64 + -3 + -32x + 4x2 = 3 + -3 Combine like terms: 64 + -3 = 61 61 + -32x + 4x2 = 3 + -3 Combine like terms: 3 + -3 = 0 61 + -32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 15.25 + -8x + x2 = 0 Move the constant term to the right: Add '-15.25' to each side of the equation. 15.25 + -8x + -15.25 + x2 = 0 + -15.25 Reorder the terms: 15.25 + -15.25 + -8x + x2 = 0 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + -8x + x2 = 0 + -15.25 -8x + x2 = 0 + -15.25 Combine like terms: 0 + -15.25 = -15.25 -8x + x2 = -15.25 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -15.25 + 16 Reorder the terms: 16 + -8x + x2 = -15.25 + 16 Combine like terms: -15.25 + 16 = 0.75 16 + -8x + x2 = 0.75 Factor a perfect square on the left side: (x + -4)(x + -4) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + -4) equal to 0.866025404 and -0.866025404.Subproblem 1
x + -4 = 0.866025404 Simplifying x + -4 = 0.866025404 Reorder the terms: -4 + x = 0.866025404 Solving -4 + x = 0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0.866025404 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0.866025404 + 4 x = 0.866025404 + 4 Combine like terms: 0.866025404 + 4 = 4.866025404 x = 4.866025404 Simplifying x = 4.866025404Subproblem 2
x + -4 = -0.866025404 Simplifying x + -4 = -0.866025404 Reorder the terms: -4 + x = -0.866025404 Solving -4 + x = -0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -0.866025404 + 4 Combine like terms: -4 + 4 = 0 0 + x = -0.866025404 + 4 x = -0.866025404 + 4 Combine like terms: -0.866025404 + 4 = 3.133974596 x = 3.133974596 Simplifying x = 3.133974596Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.866025404, 3.133974596}
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