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Simplifying 169 = 28.18x + x2 Solving 169 = 28.18x + x2 Solving for variable 'x'. Reorder the terms: 169 + -28.18x + -1x2 = 28.18x + -28.18x + x2 + -1x2 Combine like terms: 28.18x + -28.18x = 0.00 169 + -28.18x + -1x2 = 0.00 + x2 + -1x2 169 + -28.18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 169 + -28.18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -169 + 28.18x + x2 = 0 Move the constant term to the right: Add '169' to each side of the equation. -169 + 28.18x + 169 + x2 = 0 + 169 Reorder the terms: -169 + 169 + 28.18x + x2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + 28.18x + x2 = 0 + 169 28.18x + x2 = 0 + 169 Combine like terms: 0 + 169 = 169 28.18x + x2 = 169 The x term is 28.18x. Take half its coefficient (14.09). Square it (198.5281) and add it to both sides. Add '198.5281' to each side of the equation. 28.18x + 198.5281 + x2 = 169 + 198.5281 Reorder the terms: 198.5281 + 28.18x + x2 = 169 + 198.5281 Combine like terms: 169 + 198.5281 = 367.5281 198.5281 + 28.18x + x2 = 367.5281 Factor a perfect square on the left side: (x + 14.09)(x + 14.09) = 367.5281 Calculate the square root of the right side: 19.171022404 Break this problem into two subproblems by setting (x + 14.09) equal to 19.171022404 and -19.171022404.Subproblem 1
x + 14.09 = 19.171022404 Simplifying x + 14.09 = 19.171022404 Reorder the terms: 14.09 + x = 19.171022404 Solving 14.09 + x = 19.171022404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.09' to each side of the equation. 14.09 + -14.09 + x = 19.171022404 + -14.09 Combine like terms: 14.09 + -14.09 = 0.00 0.00 + x = 19.171022404 + -14.09 x = 19.171022404 + -14.09 Combine like terms: 19.171022404 + -14.09 = 5.081022404 x = 5.081022404 Simplifying x = 5.081022404Subproblem 2
x + 14.09 = -19.171022404 Simplifying x + 14.09 = -19.171022404 Reorder the terms: 14.09 + x = -19.171022404 Solving 14.09 + x = -19.171022404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.09' to each side of the equation. 14.09 + -14.09 + x = -19.171022404 + -14.09 Combine like terms: 14.09 + -14.09 = 0.00 0.00 + x = -19.171022404 + -14.09 x = -19.171022404 + -14.09 Combine like terms: -19.171022404 + -14.09 = -33.261022404 x = -33.261022404 Simplifying x = -33.261022404Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.081022404, -33.261022404}
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