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Simplifying -1x2 + 25x + -12 = 0 Reorder the terms: -12 + 25x + -1x2 = 0 Solving -12 + 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'. 12 + -25x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -25x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -25x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -25x + x2 = 0 + -12 -25x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -25x + x2 = -12 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 = -12 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -12 + 156.25 Combine like terms: -12 + 156.25 = 144.25 156.25 + -25x + x2 = 144.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (x + -12.5) equal to 12.010412149 and -12.010412149.Subproblem 1
x + -12.5 = 12.010412149 Simplifying x + -12.5 = 12.010412149 Reorder the terms: -12.5 + x = 12.010412149 Solving -12.5 + x = 12.010412149 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 = 12.010412149 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.010412149 + 12.5 x = 12.010412149 + 12.5 Combine like terms: 12.010412149 + 12.5 = 24.510412149 x = 24.510412149 Simplifying x = 24.510412149Subproblem 2
x + -12.5 = -12.010412149 Simplifying x + -12.5 = -12.010412149 Reorder the terms: -12.5 + x = -12.010412149 Solving -12.5 + x = -12.010412149 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 = -12.010412149 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.010412149 + 12.5 x = -12.010412149 + 12.5 Combine like terms: -12.010412149 + 12.5 = 0.489587851 x = 0.489587851 Simplifying x = 0.489587851Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.510412149, 0.489587851}
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