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Simplifying 4x2 + 5x = 504 Reorder the terms: 5x + 4x2 = 504 Solving 5x + 4x2 = 504 Solving for variable 'x'. Reorder the terms: -504 + 5x + 4x2 = 504 + -504 Combine like terms: 504 + -504 = 0 -504 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -126 + 1.25x + x2 = 0 Move the constant term to the right: Add '126' to each side of the equation. -126 + 1.25x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + 1.25x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 1.25x + x2 = 0 + 126 1.25x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 1.25x + x2 = 126 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 = 126 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 126 + 0.390625 Combine like terms: 126 + 0.390625 = 126.390625 0.390625 + 1.25x + x2 = 126.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 126.390625 Calculate the square root of the right side: 11.242358516 Break this problem into two subproblems by setting (x + 0.625) equal to 11.242358516 and -11.242358516.Subproblem 1
x + 0.625 = 11.242358516 Simplifying x + 0.625 = 11.242358516 Reorder the terms: 0.625 + x = 11.242358516 Solving 0.625 + x = 11.242358516 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 = 11.242358516 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 11.242358516 + -0.625 x = 11.242358516 + -0.625 Combine like terms: 11.242358516 + -0.625 = 10.617358516 x = 10.617358516 Simplifying x = 10.617358516Subproblem 2
x + 0.625 = -11.242358516 Simplifying x + 0.625 = -11.242358516 Reorder the terms: 0.625 + x = -11.242358516 Solving 0.625 + x = -11.242358516 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 = -11.242358516 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -11.242358516 + -0.625 x = -11.242358516 + -0.625 Combine like terms: -11.242358516 + -0.625 = -11.867358516 x = -11.867358516 Simplifying x = -11.867358516Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.617358516, -11.867358516}
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