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Simplifying 180 = 28x + (x * x) Multiply x * x 180 = 28x + (x2) 180 = 28x + x2 Solving 180 = 28x + x2 Solving for variable 'x'. Reorder the terms: 180 + -28x + -1x2 = 28x + -28x + x2 + -1x2 Combine like terms: 28x + -28x = 0 180 + -28x + -1x2 = 0 + x2 + -1x2 180 + -28x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 180 + -28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -180 + 28x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 28x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 28x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 28x + x2 = 0 + 180 28x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 28x + x2 = 180 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 180 + 196 Reorder the terms: 196 + 28x + x2 = 180 + 196 Combine like terms: 180 + 196 = 376 196 + 28x + x2 = 376 Factor a perfect square on the left side: (x + 14)(x + 14) = 376 Calculate the square root of the right side: 19.39071943 Break this problem into two subproblems by setting (x + 14) equal to 19.39071943 and -19.39071943.Subproblem 1
x + 14 = 19.39071943 Simplifying x + 14 = 19.39071943 Reorder the terms: 14 + x = 19.39071943 Solving 14 + x = 19.39071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 19.39071943 + -14 Combine like terms: 14 + -14 = 0 0 + x = 19.39071943 + -14 x = 19.39071943 + -14 Combine like terms: 19.39071943 + -14 = 5.39071943 x = 5.39071943 Simplifying x = 5.39071943Subproblem 2
x + 14 = -19.39071943 Simplifying x + 14 = -19.39071943 Reorder the terms: 14 + x = -19.39071943 Solving 14 + x = -19.39071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -19.39071943 + -14 Combine like terms: 14 + -14 = 0 0 + x = -19.39071943 + -14 x = -19.39071943 + -14 Combine like terms: -19.39071943 + -14 = -33.39071943 x = -33.39071943 Simplifying x = -33.39071943Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.39071943, -33.39071943}
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