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Simplifying 5x2 + -90x + 144 = 0 Reorder the terms: 144 + -90x + 5x2 = 0 Solving 144 + -90x + 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'. 28.8 + -18x + x2 = 0 Move the constant term to the right: Add '-28.8' to each side of the equation. 28.8 + -18x + -28.8 + x2 = 0 + -28.8 Reorder the terms: 28.8 + -28.8 + -18x + x2 = 0 + -28.8 Combine like terms: 28.8 + -28.8 = 0.0 0.0 + -18x + x2 = 0 + -28.8 -18x + x2 = 0 + -28.8 Combine like terms: 0 + -28.8 = -28.8 -18x + x2 = -28.8 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -28.8 + 81 Reorder the terms: 81 + -18x + x2 = -28.8 + 81 Combine like terms: -28.8 + 81 = 52.2 81 + -18x + x2 = 52.2 Factor a perfect square on the left side: (x + -9)(x + -9) = 52.2 Calculate the square root of the right side: 7.224956747 Break this problem into two subproblems by setting (x + -9) equal to 7.224956747 and -7.224956747.Subproblem 1
x + -9 = 7.224956747 Simplifying x + -9 = 7.224956747 Reorder the terms: -9 + x = 7.224956747 Solving -9 + x = 7.224956747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 7.224956747 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.224956747 + 9 x = 7.224956747 + 9 Combine like terms: 7.224956747 + 9 = 16.224956747 x = 16.224956747 Simplifying x = 16.224956747Subproblem 2
x + -9 = -7.224956747 Simplifying x + -9 = -7.224956747 Reorder the terms: -9 + x = -7.224956747 Solving -9 + x = -7.224956747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -7.224956747 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.224956747 + 9 x = -7.224956747 + 9 Combine like terms: -7.224956747 + 9 = 1.775043253 x = 1.775043253 Simplifying x = 1.775043253Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.224956747, 1.775043253}
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