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Simplifying -1x2 + 25x + -40 = 0 Reorder the terms: -40 + 25x + -1x2 = 0 Solving -40 + 25x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40 + -25x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -25x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -25x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -25x + x2 = 0 + -40 -25x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -25x + x2 = -40 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -40 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -40 + 156.25 Combine like terms: -40 + 156.25 = 116.25 156.25 + -25x + x2 = 116.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 116.25 Calculate the square root of the right side: 10.781929326 Break this problem into two subproblems by setting (x + -12.5) equal to 10.781929326 and -10.781929326.Subproblem 1
x + -12.5 = 10.781929326 Simplifying x + -12.5 = 10.781929326 Reorder the terms: -12.5 + x = 10.781929326 Solving -12.5 + x = 10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 10.781929326 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 10.781929326 + 12.5 x = 10.781929326 + 12.5 Combine like terms: 10.781929326 + 12.5 = 23.281929326 x = 23.281929326 Simplifying x = 23.281929326Subproblem 2
x + -12.5 = -10.781929326 Simplifying x + -12.5 = -10.781929326 Reorder the terms: -12.5 + x = -10.781929326 Solving -12.5 + x = -10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -10.781929326 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -10.781929326 + 12.5 x = -10.781929326 + 12.5 Combine like terms: -10.781929326 + 12.5 = 1.718070674 x = 1.718070674 Simplifying x = 1.718070674Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.281929326, 1.718070674}
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