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Simplifying x(x + -28) = 180 Reorder the terms: x(-28 + x) = 180 (-28 * x + x * x) = 180 (-28x + x2) = 180 Solving -28x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -28x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -28x + x2 = 0 Begin completing the square. 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 = 33.39071943 x = 33.39071943 Simplifying x = 33.39071943Subproblem 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 = -5.39071943 x = -5.39071943 Simplifying x = -5.39071943Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.39071943, -5.39071943}
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