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Simplifying 3(x + -2)(x + -2) = (13 + -7x)(13 + -7x) Reorder the terms: 3(-2 + x)(x + -2) = (13 + -7x)(13 + -7x) Reorder the terms: 3(-2 + x)(-2 + x) = (13 + -7x)(13 + -7x) Multiply (-2 + x) * (-2 + x) 3(-2(-2 + x) + x(-2 + x)) = (13 + -7x)(13 + -7x) 3((-2 * -2 + x * -2) + x(-2 + x)) = (13 + -7x)(13 + -7x) 3((4 + -2x) + x(-2 + x)) = (13 + -7x)(13 + -7x) 3(4 + -2x + (-2 * x + x * x)) = (13 + -7x)(13 + -7x) 3(4 + -2x + (-2x + x2)) = (13 + -7x)(13 + -7x) Combine like terms: -2x + -2x = -4x 3(4 + -4x + x2) = (13 + -7x)(13 + -7x) (4 * 3 + -4x * 3 + x2 * 3) = (13 + -7x)(13 + -7x) (12 + -12x + 3x2) = (13 + -7x)(13 + -7x) Multiply (13 + -7x) * (13 + -7x) 12 + -12x + 3x2 = (13(13 + -7x) + -7x * (13 + -7x)) 12 + -12x + 3x2 = ((13 * 13 + -7x * 13) + -7x * (13 + -7x)) 12 + -12x + 3x2 = ((169 + -91x) + -7x * (13 + -7x)) 12 + -12x + 3x2 = (169 + -91x + (13 * -7x + -7x * -7x)) 12 + -12x + 3x2 = (169 + -91x + (-91x + 49x2)) Combine like terms: -91x + -91x = -182x 12 + -12x + 3x2 = (169 + -182x + 49x2) Solving 12 + -12x + 3x2 = 169 + -182x + 49x2 Solving for variable 'x'. Reorder the terms: 12 + -169 + -12x + 182x + 3x2 + -49x2 = 169 + -182x + 49x2 + -169 + 182x + -49x2 Combine like terms: 12 + -169 = -157 -157 + -12x + 182x + 3x2 + -49x2 = 169 + -182x + 49x2 + -169 + 182x + -49x2 Combine like terms: -12x + 182x = 170x -157 + 170x + 3x2 + -49x2 = 169 + -182x + 49x2 + -169 + 182x + -49x2 Combine like terms: 3x2 + -49x2 = -46x2 -157 + 170x + -46x2 = 169 + -182x + 49x2 + -169 + 182x + -49x2 Reorder the terms: -157 + 170x + -46x2 = 169 + -169 + -182x + 182x + 49x2 + -49x2 Combine like terms: 169 + -169 = 0 -157 + 170x + -46x2 = 0 + -182x + 182x + 49x2 + -49x2 -157 + 170x + -46x2 = -182x + 182x + 49x2 + -49x2 Combine like terms: -182x + 182x = 0 -157 + 170x + -46x2 = 0 + 49x2 + -49x2 -157 + 170x + -46x2 = 49x2 + -49x2 Combine like terms: 49x2 + -49x2 = 0 -157 + 170x + -46x2 = 0 Begin completing the square. Divide all terms by -46 the coefficient of the squared term: Divide each side by '-46'. 3.413043478 + -3.695652174x + x2 = 0 Move the constant term to the right: Add '-3.413043478' to each side of the equation. 3.413043478 + -3.695652174x + -3.413043478 + x2 = 0 + -3.413043478 Reorder the terms: 3.413043478 + -3.413043478 + -3.695652174x + x2 = 0 + -3.413043478 Combine like terms: 3.413043478 + -3.413043478 = 0.000000000 0.000000000 + -3.695652174x + x2 = 0 + -3.413043478 -3.695652174x + x2 = 0 + -3.413043478 Combine like terms: 0 + -3.413043478 = -3.413043478 -3.695652174x + x2 = -3.413043478 The x term is -3.695652174x. Take half its coefficient (-1.847826087). Square it (3.414461248) and add it to both sides. Add '3.414461248' to each side of the equation. -3.695652174x + 3.414461248 + x2 = -3.413043478 + 3.414461248 Reorder the terms: 3.414461248 + -3.695652174x + x2 = -3.413043478 + 3.414461248 Combine like terms: -3.413043478 + 3.414461248 = 0.00141777 3.414461248 + -3.695652174x + x2 = 0.00141777 Factor a perfect square on the left side: (x + -1.847826087)(x + -1.847826087) = 0.00141777 Calculate the square root of the right side: 0.037653287 Break this problem into two subproblems by setting (x + -1.847826087) equal to 0.037653287 and -0.037653287.Subproblem 1
x + -1.847826087 = 0.037653287 Simplifying x + -1.847826087 = 0.037653287 Reorder the terms: -1.847826087 + x = 0.037653287 Solving -1.847826087 + x = 0.037653287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.847826087' to each side of the equation. -1.847826087 + 1.847826087 + x = 0.037653287 + 1.847826087 Combine like terms: -1.847826087 + 1.847826087 = 0.000000000 0.000000000 + x = 0.037653287 + 1.847826087 x = 0.037653287 + 1.847826087 Combine like terms: 0.037653287 + 1.847826087 = 1.885479374 x = 1.885479374 Simplifying x = 1.885479374Subproblem 2
x + -1.847826087 = -0.037653287 Simplifying x + -1.847826087 = -0.037653287 Reorder the terms: -1.847826087 + x = -0.037653287 Solving -1.847826087 + x = -0.037653287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.847826087' to each side of the equation. -1.847826087 + 1.847826087 + x = -0.037653287 + 1.847826087 Combine like terms: -1.847826087 + 1.847826087 = 0.000000000 0.000000000 + x = -0.037653287 + 1.847826087 x = -0.037653287 + 1.847826087 Combine like terms: -0.037653287 + 1.847826087 = 1.8101728 x = 1.8101728 Simplifying x = 1.8101728Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.885479374, 1.8101728}
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