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Simplifying 4x2 + 5x + -590 = 0 Reorder the terms: -590 + 5x + 4x2 = 0 Solving -590 + 5x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -147.5 + 1.25x + x2 = 0 Move the constant term to the right: Add '147.5' to each side of the equation. -147.5 + 1.25x + 147.5 + x2 = 0 + 147.5 Reorder the terms: -147.5 + 147.5 + 1.25x + x2 = 0 + 147.5 Combine like terms: -147.5 + 147.5 = 0.0 0.0 + 1.25x + x2 = 0 + 147.5 1.25x + x2 = 0 + 147.5 Combine like terms: 0 + 147.5 = 147.5 1.25x + x2 = 147.5 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 = 147.5 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 147.5 + 0.390625 Combine like terms: 147.5 + 0.390625 = 147.890625 0.390625 + 1.25x + x2 = 147.890625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 147.890625 Calculate the square root of the right side: 12.161028945 Break this problem into two subproblems by setting (x + 0.625) equal to 12.161028945 and -12.161028945.Subproblem 1
x + 0.625 = 12.161028945 Simplifying x + 0.625 = 12.161028945 Reorder the terms: 0.625 + x = 12.161028945 Solving 0.625 + x = 12.161028945 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 = 12.161028945 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 12.161028945 + -0.625 x = 12.161028945 + -0.625 Combine like terms: 12.161028945 + -0.625 = 11.536028945 x = 11.536028945 Simplifying x = 11.536028945Subproblem 2
x + 0.625 = -12.161028945 Simplifying x + 0.625 = -12.161028945 Reorder the terms: 0.625 + x = -12.161028945 Solving 0.625 + x = -12.161028945 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 = -12.161028945 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -12.161028945 + -0.625 x = -12.161028945 + -0.625 Combine like terms: -12.161028945 + -0.625 = -12.786028945 x = -12.786028945 Simplifying x = -12.786028945Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.536028945, -12.786028945}
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