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Simplifying 4x2 + 5x + -59 = 0 Reorder the terms: -59 + 5x + 4x2 = 0 Solving -59 + 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'. -14.75 + 1.25x + x2 = 0 Move the constant term to the right: Add '14.75' to each side of the equation. -14.75 + 1.25x + 14.75 + x2 = 0 + 14.75 Reorder the terms: -14.75 + 14.75 + 1.25x + x2 = 0 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + 1.25x + x2 = 0 + 14.75 1.25x + x2 = 0 + 14.75 Combine like terms: 0 + 14.75 = 14.75 1.25x + x2 = 14.75 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 = 14.75 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 14.75 + 0.390625 Combine like terms: 14.75 + 0.390625 = 15.140625 0.390625 + 1.25x + x2 = 15.140625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 15.140625 Calculate the square root of the right side: 3.891095604 Break this problem into two subproblems by setting (x + 0.625) equal to 3.891095604 and -3.891095604.Subproblem 1
x + 0.625 = 3.891095604 Simplifying x + 0.625 = 3.891095604 Reorder the terms: 0.625 + x = 3.891095604 Solving 0.625 + x = 3.891095604 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 = 3.891095604 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 3.891095604 + -0.625 x = 3.891095604 + -0.625 Combine like terms: 3.891095604 + -0.625 = 3.266095604 x = 3.266095604 Simplifying x = 3.266095604Subproblem 2
x + 0.625 = -3.891095604 Simplifying x + 0.625 = -3.891095604 Reorder the terms: 0.625 + x = -3.891095604 Solving 0.625 + x = -3.891095604 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 = -3.891095604 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -3.891095604 + -0.625 x = -3.891095604 + -0.625 Combine like terms: -3.891095604 + -0.625 = -4.516095604 x = -4.516095604 Simplifying x = -4.516095604Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.266095604, -4.516095604}
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