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Simplifying (11x2) + -1(15x) + -52 = 0 Remove parenthesis around (15x) (11x2) + -1 * 15x + -52 = 0 Multiply -1 * 15 (11x2) + -15x + -52 = 0 Reorder the terms: -52 + -15x + (11x2) = 0 Solving -52 + -15x + (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'. -4.727272727 + -1.363636364x + x2 = 0 Move the constant term to the right: Add '4.727272727' to each side of the equation. -4.727272727 + -1.363636364x + 4.727272727 + x2 = 0 + 4.727272727 Reorder the terms: -4.727272727 + 4.727272727 + -1.363636364x + x2 = 0 + 4.727272727 Combine like terms: -4.727272727 + 4.727272727 = 0.000000000 0.000000000 + -1.363636364x + x2 = 0 + 4.727272727 -1.363636364x + x2 = 0 + 4.727272727 Combine like terms: 0 + 4.727272727 = 4.727272727 -1.363636364x + x2 = 4.727272727 The x term is -1.363636364x. Take half its coefficient (-0.681818182). Square it (0.4648760333) and add it to both sides. Add '0.4648760333' to each side of the equation. -1.363636364x + 0.4648760333 + x2 = 4.727272727 + 0.4648760333 Reorder the terms: 0.4648760333 + -1.363636364x + x2 = 4.727272727 + 0.4648760333 Combine like terms: 4.727272727 + 0.4648760333 = 5.1921487603 0.4648760333 + -1.363636364x + x2 = 5.1921487603 Factor a perfect square on the left side: ((x) + -0.681818182)((x) + -0.681818182) = 5.1921487603 Calculate the square root of the right side: 2.278628702 Break this problem into two subproblems by setting ((x) + -0.681818182) equal to 2.278628702 and -2.278628702.Subproblem 1
(x) + -0.681818182 = 2.278628702 Simplifying (x) + -0.681818182 = 2.278628702 x + -0.681818182 = 2.278628702 Reorder the terms: -0.681818182 + x = 2.278628702 Solving -0.681818182 + x = 2.278628702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.681818182' to each side of the equation. -0.681818182 + 0.681818182 + x = 2.278628702 + 0.681818182 Combine like terms: -0.681818182 + 0.681818182 = 0.000000000 0.000000000 + x = 2.278628702 + 0.681818182 x = 2.278628702 + 0.681818182 Combine like terms: 2.278628702 + 0.681818182 = 2.960446884 x = 2.960446884 Simplifying x = 2.960446884Subproblem 2
(x) + -0.681818182 = -2.278628702 Simplifying (x) + -0.681818182 = -2.278628702 x + -0.681818182 = -2.278628702 Reorder the terms: -0.681818182 + x = -2.278628702 Solving -0.681818182 + x = -2.278628702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.681818182' to each side of the equation. -0.681818182 + 0.681818182 + x = -2.278628702 + 0.681818182 Combine like terms: -0.681818182 + 0.681818182 = 0.000000000 0.000000000 + x = -2.278628702 + 0.681818182 x = -2.278628702 + 0.681818182 Combine like terms: -2.278628702 + 0.681818182 = -1.59681052 x = -1.59681052 Simplifying x = -1.59681052Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.960446884, -1.59681052}
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