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Simplifying -5x2 + 72x + 124 = 0 Reorder the terms: 124 + 72x + -5x2 = 0 Solving 124 + 72x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -24.8 + -14.4x + x2 = 0 Move the constant term to the right: Add '24.8' to each side of the equation. -24.8 + -14.4x + 24.8 + x2 = 0 + 24.8 Reorder the terms: -24.8 + 24.8 + -14.4x + x2 = 0 + 24.8 Combine like terms: -24.8 + 24.8 = 0.0 0.0 + -14.4x + x2 = 0 + 24.8 -14.4x + x2 = 0 + 24.8 Combine like terms: 0 + 24.8 = 24.8 -14.4x + x2 = 24.8 The x term is -14.4x. Take half its coefficient (-7.2). Square it (51.84) and add it to both sides. Add '51.84' to each side of the equation. -14.4x + 51.84 + x2 = 24.8 + 51.84 Reorder the terms: 51.84 + -14.4x + x2 = 24.8 + 51.84 Combine like terms: 24.8 + 51.84 = 76.64 51.84 + -14.4x + x2 = 76.64 Factor a perfect square on the left side: (x + -7.2)(x + -7.2) = 76.64 Calculate the square root of the right side: 8.754427451 Break this problem into two subproblems by setting (x + -7.2) equal to 8.754427451 and -8.754427451.Subproblem 1
x + -7.2 = 8.754427451 Simplifying x + -7.2 = 8.754427451 Reorder the terms: -7.2 + x = 8.754427451 Solving -7.2 + x = 8.754427451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = 8.754427451 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = 8.754427451 + 7.2 x = 8.754427451 + 7.2 Combine like terms: 8.754427451 + 7.2 = 15.954427451 x = 15.954427451 Simplifying x = 15.954427451Subproblem 2
x + -7.2 = -8.754427451 Simplifying x + -7.2 = -8.754427451 Reorder the terms: -7.2 + x = -8.754427451 Solving -7.2 + x = -8.754427451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = -8.754427451 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = -8.754427451 + 7.2 x = -8.754427451 + 7.2 Combine like terms: -8.754427451 + 7.2 = -1.554427451 x = -1.554427451 Simplifying x = -1.554427451Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.954427451, -1.554427451}
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