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Simplifying x(x + -36) = 5950 Reorder the terms: x(-36 + x) = 5950 (-36 * x + x * x) = 5950 (-36x + x2) = 5950 Solving -36x + x2 = 5950 Solving for variable 'x'. Reorder the terms: -5950 + -36x + x2 = 5950 + -5950 Combine like terms: 5950 + -5950 = 0 -5950 + -36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5950' to each side of the equation. -5950 + -36x + 5950 + x2 = 0 + 5950 Reorder the terms: -5950 + 5950 + -36x + x2 = 0 + 5950 Combine like terms: -5950 + 5950 = 0 0 + -36x + x2 = 0 + 5950 -36x + x2 = 0 + 5950 Combine like terms: 0 + 5950 = 5950 -36x + x2 = 5950 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = 5950 + 324 Reorder the terms: 324 + -36x + x2 = 5950 + 324 Combine like terms: 5950 + 324 = 6274 324 + -36x + x2 = 6274 Factor a perfect square on the left side: (x + -18)(x + -18) = 6274 Calculate the square root of the right side: 79.208585393 Break this problem into two subproblems by setting (x + -18) equal to 79.208585393 and -79.208585393.Subproblem 1
x + -18 = 79.208585393 Simplifying x + -18 = 79.208585393 Reorder the terms: -18 + x = 79.208585393 Solving -18 + x = 79.208585393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 79.208585393 + 18 Combine like terms: -18 + 18 = 0 0 + x = 79.208585393 + 18 x = 79.208585393 + 18 Combine like terms: 79.208585393 + 18 = 97.208585393 x = 97.208585393 Simplifying x = 97.208585393Subproblem 2
x + -18 = -79.208585393 Simplifying x + -18 = -79.208585393 Reorder the terms: -18 + x = -79.208585393 Solving -18 + x = -79.208585393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -79.208585393 + 18 Combine like terms: -18 + 18 = 0 0 + x = -79.208585393 + 18 x = -79.208585393 + 18 Combine like terms: -79.208585393 + 18 = -61.208585393 x = -61.208585393 Simplifying x = -61.208585393Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.208585393, -61.208585393}
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