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Simplifying 315 = (x + 20)(x)(5) Reorder the terms: 315 = (20 + x)(x)(5) Reorder the terms for easier multiplication: 315 = 5x(20 + x) 315 = (20 * 5x + x * 5x) 315 = (100x + 5x2) Solving 315 = 100x + 5x2 Solving for variable 'x'. Reorder the terms: 315 + -100x + -5x2 = 100x + -100x + 5x2 + -5x2 Combine like terms: 100x + -100x = 0 315 + -100x + -5x2 = 0 + 5x2 + -5x2 315 + -100x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 315 + -100x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(63 + -20x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(63 + -20x + -1x2)' equal to zero and attempt to solve: Simplifying 63 + -20x + -1x2 = 0 Solving 63 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + 20x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 20x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 20x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 20x + x2 = 0 + 63 20x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 20x + x2 = 63 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 63 + 100 Reorder the terms: 100 + 20x + x2 = 63 + 100 Combine like terms: 63 + 100 = 163 100 + 20x + x2 = 163 Factor a perfect square on the left side: (x + 10)(x + 10) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (x + 10) equal to 12.767145335 and -12.767145335.Subproblem 1
x + 10 = 12.767145335 Simplifying x + 10 = 12.767145335 Reorder the terms: 10 + x = 12.767145335 Solving 10 + x = 12.767145335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 12.767145335 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.767145335 + -10 x = 12.767145335 + -10 Combine like terms: 12.767145335 + -10 = 2.767145335 x = 2.767145335 Simplifying x = 2.767145335Subproblem 2
x + 10 = -12.767145335 Simplifying x + 10 = -12.767145335 Reorder the terms: 10 + x = -12.767145335 Solving 10 + x = -12.767145335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -12.767145335 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.767145335 + -10 x = -12.767145335 + -10 Combine like terms: -12.767145335 + -10 = -22.767145335 x = -22.767145335 Simplifying x = -22.767145335Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.767145335, -22.767145335}Solution
x = {2.767145335, -22.767145335}
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