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Simplifying -5x2 + 72x + 502 = 0 Reorder the terms: 502 + 72x + -5x2 = 0 Solving 502 + 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'. -100.4 + -14.4x + x2 = 0 Move the constant term to the right: Add '100.4' to each side of the equation. -100.4 + -14.4x + 100.4 + x2 = 0 + 100.4 Reorder the terms: -100.4 + 100.4 + -14.4x + x2 = 0 + 100.4 Combine like terms: -100.4 + 100.4 = 0.0 0.0 + -14.4x + x2 = 0 + 100.4 -14.4x + x2 = 0 + 100.4 Combine like terms: 0 + 100.4 = 100.4 -14.4x + x2 = 100.4 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 = 100.4 + 51.84 Reorder the terms: 51.84 + -14.4x + x2 = 100.4 + 51.84 Combine like terms: 100.4 + 51.84 = 152.24 51.84 + -14.4x + x2 = 152.24 Factor a perfect square on the left side: (x + -7.2)(x + -7.2) = 152.24 Calculate the square root of the right side: 12.338557452 Break this problem into two subproblems by setting (x + -7.2) equal to 12.338557452 and -12.338557452.Subproblem 1
x + -7.2 = 12.338557452 Simplifying x + -7.2 = 12.338557452 Reorder the terms: -7.2 + x = 12.338557452 Solving -7.2 + x = 12.338557452 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 = 12.338557452 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = 12.338557452 + 7.2 x = 12.338557452 + 7.2 Combine like terms: 12.338557452 + 7.2 = 19.538557452 x = 19.538557452 Simplifying x = 19.538557452Subproblem 2
x + -7.2 = -12.338557452 Simplifying x + -7.2 = -12.338557452 Reorder the terms: -7.2 + x = -12.338557452 Solving -7.2 + x = -12.338557452 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 = -12.338557452 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = -12.338557452 + 7.2 x = -12.338557452 + 7.2 Combine like terms: -12.338557452 + 7.2 = -5.138557452 x = -5.138557452 Simplifying x = -5.138557452Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.538557452, -5.138557452}
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