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Simplifying -11x2 + -5x + 70 = 0 Reorder the terms: 70 + -5x + -11x2 = 0 Solving 70 + -5x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -6.363636364 + 0.4545454545x + x2 = 0 Move the constant term to the right: Add '6.363636364' to each side of the equation. -6.363636364 + 0.4545454545x + 6.363636364 + x2 = 0 + 6.363636364 Reorder the terms: -6.363636364 + 6.363636364 + 0.4545454545x + x2 = 0 + 6.363636364 Combine like terms: -6.363636364 + 6.363636364 = 0.000000000 0.000000000 + 0.4545454545x + x2 = 0 + 6.363636364 0.4545454545x + x2 = 0 + 6.363636364 Combine like terms: 0 + 6.363636364 = 6.363636364 0.4545454545x + x2 = 6.363636364 The x term is 0.4545454545x. Take half its coefficient (0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. 0.4545454545x + 0.05165289257 + x2 = 6.363636364 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545x + x2 = 6.363636364 + 0.05165289257 Combine like terms: 6.363636364 + 0.05165289257 = 6.41528925657 0.05165289257 + 0.4545454545x + x2 = 6.41528925657 Factor a perfect square on the left side: (x + 0.2272727273)(x + 0.2272727273) = 6.41528925657 Calculate the square root of the right side: 2.53284213 Break this problem into two subproblems by setting (x + 0.2272727273) equal to 2.53284213 and -2.53284213.Subproblem 1
x + 0.2272727273 = 2.53284213 Simplifying x + 0.2272727273 = 2.53284213 Reorder the terms: 0.2272727273 + x = 2.53284213 Solving 0.2272727273 + x = 2.53284213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = 2.53284213 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = 2.53284213 + -0.2272727273 x = 2.53284213 + -0.2272727273 Combine like terms: 2.53284213 + -0.2272727273 = 2.3055694027 x = 2.3055694027 Simplifying x = 2.3055694027Subproblem 2
x + 0.2272727273 = -2.53284213 Simplifying x + 0.2272727273 = -2.53284213 Reorder the terms: 0.2272727273 + x = -2.53284213 Solving 0.2272727273 + x = -2.53284213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = -2.53284213 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = -2.53284213 + -0.2272727273 x = -2.53284213 + -0.2272727273 Combine like terms: -2.53284213 + -0.2272727273 = -2.7601148573 x = -2.7601148573 Simplifying x = -2.7601148573Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3055694027, -2.7601148573}
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