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Simplifying 4x2 + 5x + -936 = 0 Reorder the terms: -936 + 5x + 4x2 = 0 Solving -936 + 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'. -234 + 1.25x + x2 = 0 Move the constant term to the right: Add '234' to each side of the equation. -234 + 1.25x + 234 + x2 = 0 + 234 Reorder the terms: -234 + 234 + 1.25x + x2 = 0 + 234 Combine like terms: -234 + 234 = 0 0 + 1.25x + x2 = 0 + 234 1.25x + x2 = 0 + 234 Combine like terms: 0 + 234 = 234 1.25x + x2 = 234 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 = 234 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 234 + 0.390625 Combine like terms: 234 + 0.390625 = 234.390625 0.390625 + 1.25x + x2 = 234.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 234.390625 Calculate the square root of the right side: 15.309821194 Break this problem into two subproblems by setting (x + 0.625) equal to 15.309821194 and -15.309821194.Subproblem 1
x + 0.625 = 15.309821194 Simplifying x + 0.625 = 15.309821194 Reorder the terms: 0.625 + x = 15.309821194 Solving 0.625 + x = 15.309821194 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 = 15.309821194 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 15.309821194 + -0.625 x = 15.309821194 + -0.625 Combine like terms: 15.309821194 + -0.625 = 14.684821194 x = 14.684821194 Simplifying x = 14.684821194Subproblem 2
x + 0.625 = -15.309821194 Simplifying x + 0.625 = -15.309821194 Reorder the terms: 0.625 + x = -15.309821194 Solving 0.625 + x = -15.309821194 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 = -15.309821194 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -15.309821194 + -0.625 x = -15.309821194 + -0.625 Combine like terms: -15.309821194 + -0.625 = -15.934821194 x = -15.934821194 Simplifying x = -15.934821194Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.684821194, -15.934821194}
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