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Simplifying -16x2 + 225x + 20 = 0 Reorder the terms: 20 + 225x + -16x2 = 0 Solving 20 + 225x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.25 + -14.0625x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -14.0625x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -14.0625x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -14.0625x + x2 = 0 + 1.25 -14.0625x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -14.0625x + x2 = 1.25 The x term is -14.0625x. Take half its coefficient (-7.03125). Square it (49.43847656) and add it to both sides. Add '49.43847656' to each side of the equation. -14.0625x + 49.43847656 + x2 = 1.25 + 49.43847656 Reorder the terms: 49.43847656 + -14.0625x + x2 = 1.25 + 49.43847656 Combine like terms: 1.25 + 49.43847656 = 50.68847656 49.43847656 + -14.0625x + x2 = 50.68847656 Factor a perfect square on the left side: (x + -7.03125)(x + -7.03125) = 50.68847656 Calculate the square root of the right side: 7.119584016 Break this problem into two subproblems by setting (x + -7.03125) equal to 7.119584016 and -7.119584016.Subproblem 1
x + -7.03125 = 7.119584016 Simplifying x + -7.03125 = 7.119584016 Reorder the terms: -7.03125 + x = 7.119584016 Solving -7.03125 + x = 7.119584016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.03125' to each side of the equation. -7.03125 + 7.03125 + x = 7.119584016 + 7.03125 Combine like terms: -7.03125 + 7.03125 = 0.00000 0.00000 + x = 7.119584016 + 7.03125 x = 7.119584016 + 7.03125 Combine like terms: 7.119584016 + 7.03125 = 14.150834016 x = 14.150834016 Simplifying x = 14.150834016Subproblem 2
x + -7.03125 = -7.119584016 Simplifying x + -7.03125 = -7.119584016 Reorder the terms: -7.03125 + x = -7.119584016 Solving -7.03125 + x = -7.119584016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.03125' to each side of the equation. -7.03125 + 7.03125 + x = -7.119584016 + 7.03125 Combine like terms: -7.03125 + 7.03125 = 0.00000 0.00000 + x = -7.119584016 + 7.03125 x = -7.119584016 + 7.03125 Combine like terms: -7.119584016 + 7.03125 = -0.088334016 x = -0.088334016 Simplifying x = -0.088334016Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.150834016, -0.088334016}
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