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Simplifying 14x(36 + x) = -15 + -36 (36 * 14x + x * 14x) = -15 + -36 (504x + 14x2) = -15 + -36 Combine like terms: -15 + -36 = -51 504x + 14x2 = -51 Solving 504x + 14x2 = -51 Solving for variable 'x'. Reorder the terms: 51 + 504x + 14x2 = -51 + 51 Combine like terms: -51 + 51 = 0 51 + 504x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 3.642857143 + 36x + x2 = 0 Move the constant term to the right: Add '-3.642857143' to each side of the equation. 3.642857143 + 36x + -3.642857143 + x2 = 0 + -3.642857143 Reorder the terms: 3.642857143 + -3.642857143 + 36x + x2 = 0 + -3.642857143 Combine like terms: 3.642857143 + -3.642857143 = 0.000000000 0.000000000 + 36x + x2 = 0 + -3.642857143 36x + x2 = 0 + -3.642857143 Combine like terms: 0 + -3.642857143 = -3.642857143 36x + x2 = -3.642857143 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 = -3.642857143 + 324 Reorder the terms: 324 + 36x + x2 = -3.642857143 + 324 Combine like terms: -3.642857143 + 324 = 320.357142857 324 + 36x + x2 = 320.357142857 Factor a perfect square on the left side: (x + 18)(x + 18) = 320.357142857 Calculate the square root of the right side: 17.898523483 Break this problem into two subproblems by setting (x + 18) equal to 17.898523483 and -17.898523483.Subproblem 1
x + 18 = 17.898523483 Simplifying x + 18 = 17.898523483 Reorder the terms: 18 + x = 17.898523483 Solving 18 + x = 17.898523483 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 = 17.898523483 + -18 Combine like terms: 18 + -18 = 0 0 + x = 17.898523483 + -18 x = 17.898523483 + -18 Combine like terms: 17.898523483 + -18 = -0.101476517 x = -0.101476517 Simplifying x = -0.101476517Subproblem 2
x + 18 = -17.898523483 Simplifying x + 18 = -17.898523483 Reorder the terms: 18 + x = -17.898523483 Solving 18 + x = -17.898523483 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 = -17.898523483 + -18 Combine like terms: 18 + -18 = 0 0 + x = -17.898523483 + -18 x = -17.898523483 + -18 Combine like terms: -17.898523483 + -18 = -35.898523483 x = -35.898523483 Simplifying x = -35.898523483Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.101476517, -35.898523483}
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