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Simplifying 500 + -9x = 4x2 Solving 500 + -9x = 4x2 Solving for variable 'x'. Combine like terms: 4x2 + -4x2 = 0 500 + -9x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -125 + 2.25x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + 2.25x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 2.25x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 2.25x + x2 = 0 + 125 2.25x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 2.25x + x2 = 125 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 125 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 125 + 1.265625 Combine like terms: 125 + 1.265625 = 126.265625 1.265625 + 2.25x + x2 = 126.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 126.265625 Calculate the square root of the right side: 11.236797809 Break this problem into two subproblems by setting (x + 1.125) equal to 11.236797809 and -11.236797809.Subproblem 1
x + 1.125 = 11.236797809 Simplifying x + 1.125 = 11.236797809 Reorder the terms: 1.125 + x = 11.236797809 Solving 1.125 + x = 11.236797809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 11.236797809 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 11.236797809 + -1.125 x = 11.236797809 + -1.125 Combine like terms: 11.236797809 + -1.125 = 10.111797809 x = 10.111797809 Simplifying x = 10.111797809Subproblem 2
x + 1.125 = -11.236797809 Simplifying x + 1.125 = -11.236797809 Reorder the terms: 1.125 + x = -11.236797809 Solving 1.125 + x = -11.236797809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -11.236797809 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -11.236797809 + -1.125 x = -11.236797809 + -1.125 Combine like terms: -11.236797809 + -1.125 = -12.361797809 x = -12.361797809 Simplifying x = -12.361797809Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.111797809, -12.361797809}
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