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Simplifying -2x2 + -25x + 150 = 0 Reorder the terms: 150 + -25x + -2x2 = 0 Solving 150 + -25x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -75 + 12.5x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 12.5x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 12.5x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 12.5x + x2 = 0 + 75 12.5x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 12.5x + x2 = 75 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = 75 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 75 + 39.0625 Combine like terms: 75 + 39.0625 = 114.0625 39.0625 + 12.5x + x2 = 114.0625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 114.0625 Calculate the square root of the right side: 10.680004682 Break this problem into two subproblems by setting (x + 6.25) equal to 10.680004682 and -10.680004682.Subproblem 1
x + 6.25 = 10.680004682 Simplifying x + 6.25 = 10.680004682 Reorder the terms: 6.25 + x = 10.680004682 Solving 6.25 + x = 10.680004682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 10.680004682 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 10.680004682 + -6.25 x = 10.680004682 + -6.25 Combine like terms: 10.680004682 + -6.25 = 4.430004682 x = 4.430004682 Simplifying x = 4.430004682Subproblem 2
x + 6.25 = -10.680004682 Simplifying x + 6.25 = -10.680004682 Reorder the terms: 6.25 + x = -10.680004682 Solving 6.25 + x = -10.680004682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -10.680004682 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -10.680004682 + -6.25 x = -10.680004682 + -6.25 Combine like terms: -10.680004682 + -6.25 = -16.930004682 x = -16.930004682 Simplifying x = -16.930004682Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.430004682, -16.930004682}
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