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Simplifying (2x + -2)(4x + 1) = 125 Reorder the terms: (-2 + 2x)(4x + 1) = 125 Reorder the terms: (-2 + 2x)(1 + 4x) = 125 Multiply (-2 + 2x) * (1 + 4x) (-2(1 + 4x) + 2x * (1 + 4x)) = 125 ((1 * -2 + 4x * -2) + 2x * (1 + 4x)) = 125 ((-2 + -8x) + 2x * (1 + 4x)) = 125 (-2 + -8x + (1 * 2x + 4x * 2x)) = 125 (-2 + -8x + (2x + 8x2)) = 125 Combine like terms: -8x + 2x = -6x (-2 + -6x + 8x2) = 125 Solving -2 + -6x + 8x2 = 125 Solving for variable 'x'. Reorder the terms: -2 + -125 + -6x + 8x2 = 125 + -125 Combine like terms: -2 + -125 = -127 -127 + -6x + 8x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -127 + -6x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -15.875 + -0.75x + x2 = 0 Move the constant term to the right: Add '15.875' to each side of the equation. -15.875 + -0.75x + 15.875 + x2 = 0 + 15.875 Reorder the terms: -15.875 + 15.875 + -0.75x + x2 = 0 + 15.875 Combine like terms: -15.875 + 15.875 = 0.000 0.000 + -0.75x + x2 = 0 + 15.875 -0.75x + x2 = 0 + 15.875 Combine like terms: 0 + 15.875 = 15.875 -0.75x + x2 = 15.875 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 15.875 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 15.875 + 0.140625 Combine like terms: 15.875 + 0.140625 = 16.015625 0.140625 + -0.75x + x2 = 16.015625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 16.015625 Calculate the square root of the right side: 4.001952648 Break this problem into two subproblems by setting (x + -0.375) equal to 4.001952648 and -4.001952648.Subproblem 1
x + -0.375 = 4.001952648 Simplifying x + -0.375 = 4.001952648 Reorder the terms: -0.375 + x = 4.001952648 Solving -0.375 + x = 4.001952648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 4.001952648 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 4.001952648 + 0.375 x = 4.001952648 + 0.375 Combine like terms: 4.001952648 + 0.375 = 4.376952648 x = 4.376952648 Simplifying x = 4.376952648Subproblem 2
x + -0.375 = -4.001952648 Simplifying x + -0.375 = -4.001952648 Reorder the terms: -0.375 + x = -4.001952648 Solving -0.375 + x = -4.001952648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -4.001952648 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -4.001952648 + 0.375 x = -4.001952648 + 0.375 Combine like terms: -4.001952648 + 0.375 = -3.626952648 x = -3.626952648 Simplifying x = -3.626952648Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.376952648, -3.626952648}
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