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Simplifying 144 = 2x2 + 18x Reorder the terms: 144 = 18x + 2x2 Solving 144 = 18x + 2x2 Solving for variable 'x'. Reorder the terms: 144 + -18x + -2x2 = 18x + -18x + 2x2 + -2x2 Combine like terms: 18x + -18x = 0 144 + -18x + -2x2 = 0 + 2x2 + -2x2 144 + -18x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 144 + -18x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(72 + -9x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(72 + -9x + -1x2)' equal to zero and attempt to solve: Simplifying 72 + -9x + -1x2 = 0 Solving 72 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -72 + 9x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + 9x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 9x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 9x + x2 = 0 + 72 9x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 9x + x2 = 72 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 72 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 72 + 20.25 Combine like terms: 72 + 20.25 = 92.25 20.25 + 9x + x2 = 92.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (x + 4.5) equal to 9.604686356 and -9.604686356.Subproblem 1
x + 4.5 = 9.604686356 Simplifying x + 4.5 = 9.604686356 Reorder the terms: 4.5 + x = 9.604686356 Solving 4.5 + x = 9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 9.604686356 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 9.604686356 + -4.5 x = 9.604686356 + -4.5 Combine like terms: 9.604686356 + -4.5 = 5.104686356 x = 5.104686356 Simplifying x = 5.104686356Subproblem 2
x + 4.5 = -9.604686356 Simplifying x + 4.5 = -9.604686356 Reorder the terms: 4.5 + x = -9.604686356 Solving 4.5 + x = -9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -9.604686356 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -9.604686356 + -4.5 x = -9.604686356 + -4.5 Combine like terms: -9.604686356 + -4.5 = -14.104686356 x = -14.104686356 Simplifying x = -14.104686356Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.104686356, -14.104686356}Solution
x = {5.104686356, -14.104686356}
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