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Simplifying x(4x + 5) = 520 Reorder the terms: x(5 + 4x) = 520 (5 * x + 4x * x) = 520 (5x + 4x2) = 520 Solving 5x + 4x2 = 520 Solving for variable 'x'. Reorder the terms: -520 + 5x + 4x2 = 520 + -520 Combine like terms: 520 + -520 = 0 -520 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -130 + 1.25x + x2 = 0 Move the constant term to the right: Add '130' to each side of the equation. -130 + 1.25x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 1.25x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 1.25x + x2 = 0 + 130 1.25x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 1.25x + x2 = 130 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 130 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 130 + 0.390625 Combine like terms: 130 + 0.390625 = 130.390625 0.390625 + 1.25x + x2 = 130.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 130.390625 Calculate the square root of the right side: 11.418871442 Break this problem into two subproblems by setting (x + 0.625) equal to 11.418871442 and -11.418871442.Subproblem 1
x + 0.625 = 11.418871442 Simplifying x + 0.625 = 11.418871442 Reorder the terms: 0.625 + x = 11.418871442 Solving 0.625 + x = 11.418871442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 11.418871442 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 11.418871442 + -0.625 x = 11.418871442 + -0.625 Combine like terms: 11.418871442 + -0.625 = 10.793871442 x = 10.793871442 Simplifying x = 10.793871442Subproblem 2
x + 0.625 = -11.418871442 Simplifying x + 0.625 = -11.418871442 Reorder the terms: 0.625 + x = -11.418871442 Solving 0.625 + x = -11.418871442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -11.418871442 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -11.418871442 + -0.625 x = -11.418871442 + -0.625 Combine like terms: -11.418871442 + -0.625 = -12.043871442 x = -12.043871442 Simplifying x = -12.043871442Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.793871442, -12.043871442}
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