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Simplifying 46x2 + 50x + -12.5 = 0 Reorder the terms: -12.5 + 50x + 46x2 = 0 Solving -12.5 + 50x + 46x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 46 the coefficient of the squared term: Divide each side by '46'. -0.2717391304 + 1.086956522x + x2 = 0 Move the constant term to the right: Add '0.2717391304' to each side of the equation. -0.2717391304 + 1.086956522x + 0.2717391304 + x2 = 0 + 0.2717391304 Reorder the terms: -0.2717391304 + 0.2717391304 + 1.086956522x + x2 = 0 + 0.2717391304 Combine like terms: -0.2717391304 + 0.2717391304 = 0.0000000000 0.0000000000 + 1.086956522x + x2 = 0 + 0.2717391304 1.086956522x + x2 = 0 + 0.2717391304 Combine like terms: 0 + 0.2717391304 = 0.2717391304 1.086956522x + x2 = 0.2717391304 The x term is 1.086956522x. Take half its coefficient (0.543478261). Square it (0.2953686202) and add it to both sides. Add '0.2953686202' to each side of the equation. 1.086956522x + 0.2953686202 + x2 = 0.2717391304 + 0.2953686202 Reorder the terms: 0.2953686202 + 1.086956522x + x2 = 0.2717391304 + 0.2953686202 Combine like terms: 0.2717391304 + 0.2953686202 = 0.5671077506 0.2953686202 + 1.086956522x + x2 = 0.5671077506 Factor a perfect square on the left side: (x + 0.543478261)(x + 0.543478261) = 0.5671077506 Calculate the square root of the right side: 0.753065569 Break this problem into two subproblems by setting (x + 0.543478261) equal to 0.753065569 and -0.753065569.Subproblem 1
x + 0.543478261 = 0.753065569 Simplifying x + 0.543478261 = 0.753065569 Reorder the terms: 0.543478261 + x = 0.753065569 Solving 0.543478261 + x = 0.753065569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.543478261' to each side of the equation. 0.543478261 + -0.543478261 + x = 0.753065569 + -0.543478261 Combine like terms: 0.543478261 + -0.543478261 = 0.000000000 0.000000000 + x = 0.753065569 + -0.543478261 x = 0.753065569 + -0.543478261 Combine like terms: 0.753065569 + -0.543478261 = 0.209587308 x = 0.209587308 Simplifying x = 0.209587308Subproblem 2
x + 0.543478261 = -0.753065569 Simplifying x + 0.543478261 = -0.753065569 Reorder the terms: 0.543478261 + x = -0.753065569 Solving 0.543478261 + x = -0.753065569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.543478261' to each side of the equation. 0.543478261 + -0.543478261 + x = -0.753065569 + -0.543478261 Combine like terms: 0.543478261 + -0.543478261 = 0.000000000 0.000000000 + x = -0.753065569 + -0.543478261 x = -0.753065569 + -0.543478261 Combine like terms: -0.753065569 + -0.543478261 = -1.29654383 x = -1.29654383 Simplifying x = -1.29654383Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.209587308, -1.29654383}
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