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Simplifying 18x2 + 37x + -70 = 0 Reorder the terms: -70 + 37x + 18x2 = 0 Solving -70 + 37x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -3.888888889 + 2.055555556x + x2 = 0 Move the constant term to the right: Add '3.888888889' to each side of the equation. -3.888888889 + 2.055555556x + 3.888888889 + x2 = 0 + 3.888888889 Reorder the terms: -3.888888889 + 3.888888889 + 2.055555556x + x2 = 0 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + 2.055555556x + x2 = 0 + 3.888888889 2.055555556x + x2 = 0 + 3.888888889 Combine like terms: 0 + 3.888888889 = 3.888888889 2.055555556x + x2 = 3.888888889 The x term is 2.055555556x. Take half its coefficient (1.027777778). Square it (1.056327161) and add it to both sides. Add '1.056327161' to each side of the equation. 2.055555556x + 1.056327161 + x2 = 3.888888889 + 1.056327161 Reorder the terms: 1.056327161 + 2.055555556x + x2 = 3.888888889 + 1.056327161 Combine like terms: 3.888888889 + 1.056327161 = 4.94521605 1.056327161 + 2.055555556x + x2 = 4.94521605 Factor a perfect square on the left side: (x + 1.027777778)(x + 1.027777778) = 4.94521605 Calculate the square root of the right side: 2.223784173 Break this problem into two subproblems by setting (x + 1.027777778) equal to 2.223784173 and -2.223784173.Subproblem 1
x + 1.027777778 = 2.223784173 Simplifying x + 1.027777778 = 2.223784173 Reorder the terms: 1.027777778 + x = 2.223784173 Solving 1.027777778 + x = 2.223784173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.027777778' to each side of the equation. 1.027777778 + -1.027777778 + x = 2.223784173 + -1.027777778 Combine like terms: 1.027777778 + -1.027777778 = 0.000000000 0.000000000 + x = 2.223784173 + -1.027777778 x = 2.223784173 + -1.027777778 Combine like terms: 2.223784173 + -1.027777778 = 1.196006395 x = 1.196006395 Simplifying x = 1.196006395Subproblem 2
x + 1.027777778 = -2.223784173 Simplifying x + 1.027777778 = -2.223784173 Reorder the terms: 1.027777778 + x = -2.223784173 Solving 1.027777778 + x = -2.223784173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.027777778' to each side of the equation. 1.027777778 + -1.027777778 + x = -2.223784173 + -1.027777778 Combine like terms: 1.027777778 + -1.027777778 = 0.000000000 0.000000000 + x = -2.223784173 + -1.027777778 x = -2.223784173 + -1.027777778 Combine like terms: -2.223784173 + -1.027777778 = -3.251561951 x = -3.251561951 Simplifying x = -3.251561951Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.196006395, -3.251561951}
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