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Simplifying -1x2 + 25x + 140 = 0 Reorder the terms: 140 + 25x + -1x2 = 0 Solving 140 + 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'. -140 + -25x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + -25x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -25x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -25x + x2 = 0 + 140 -25x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -25x + x2 = 140 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 = 140 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 140 + 156.25 Combine like terms: 140 + 156.25 = 296.25 156.25 + -25x + x2 = 296.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 296.25 Calculate the square root of the right side: 17.211914478 Break this problem into two subproblems by setting (x + -12.5) equal to 17.211914478 and -17.211914478.Subproblem 1
x + -12.5 = 17.211914478 Simplifying x + -12.5 = 17.211914478 Reorder the terms: -12.5 + x = 17.211914478 Solving -12.5 + x = 17.211914478 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 = 17.211914478 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 17.211914478 + 12.5 x = 17.211914478 + 12.5 Combine like terms: 17.211914478 + 12.5 = 29.711914478 x = 29.711914478 Simplifying x = 29.711914478Subproblem 2
x + -12.5 = -17.211914478 Simplifying x + -12.5 = -17.211914478 Reorder the terms: -12.5 + x = -17.211914478 Solving -12.5 + x = -17.211914478 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 = -17.211914478 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -17.211914478 + 12.5 x = -17.211914478 + 12.5 Combine like terms: -17.211914478 + 12.5 = -4.711914478 x = -4.711914478 Simplifying x = -4.711914478Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.711914478, -4.711914478}
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