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Simplifying 11x2 + 150x + -500 = 0 Reorder the terms: -500 + 150x + 11x2 = 0 Solving -500 + 150x + 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'. -45.45454545 + 13.63636364x + x2 = 0 Move the constant term to the right: Add '45.45454545' to each side of the equation. -45.45454545 + 13.63636364x + 45.45454545 + x2 = 0 + 45.45454545 Reorder the terms: -45.45454545 + 45.45454545 + 13.63636364x + x2 = 0 + 45.45454545 Combine like terms: -45.45454545 + 45.45454545 = 0.00000000 0.00000000 + 13.63636364x + x2 = 0 + 45.45454545 13.63636364x + x2 = 0 + 45.45454545 Combine like terms: 0 + 45.45454545 = 45.45454545 13.63636364x + x2 = 45.45454545 The x term is 13.63636364x. Take half its coefficient (6.81818182). Square it (46.48760333) and add it to both sides. Add '46.48760333' to each side of the equation. 13.63636364x + 46.48760333 + x2 = 45.45454545 + 46.48760333 Reorder the terms: 46.48760333 + 13.63636364x + x2 = 45.45454545 + 46.48760333 Combine like terms: 45.45454545 + 46.48760333 = 91.94214878 46.48760333 + 13.63636364x + x2 = 91.94214878 Factor a perfect square on the left side: (x + 6.81818182)(x + 6.81818182) = 91.94214878 Calculate the square root of the right side: 9.588646869 Break this problem into two subproblems by setting (x + 6.81818182) equal to 9.588646869 and -9.588646869.Subproblem 1
x + 6.81818182 = 9.588646869 Simplifying x + 6.81818182 = 9.588646869 Reorder the terms: 6.81818182 + x = 9.588646869 Solving 6.81818182 + x = 9.588646869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.81818182' to each side of the equation. 6.81818182 + -6.81818182 + x = 9.588646869 + -6.81818182 Combine like terms: 6.81818182 + -6.81818182 = 0.00000000 0.00000000 + x = 9.588646869 + -6.81818182 x = 9.588646869 + -6.81818182 Combine like terms: 9.588646869 + -6.81818182 = 2.770465049 x = 2.770465049 Simplifying x = 2.770465049Subproblem 2
x + 6.81818182 = -9.588646869 Simplifying x + 6.81818182 = -9.588646869 Reorder the terms: 6.81818182 + x = -9.588646869 Solving 6.81818182 + x = -9.588646869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.81818182' to each side of the equation. 6.81818182 + -6.81818182 + x = -9.588646869 + -6.81818182 Combine like terms: 6.81818182 + -6.81818182 = 0.00000000 0.00000000 + x = -9.588646869 + -6.81818182 x = -9.588646869 + -6.81818182 Combine like terms: -9.588646869 + -6.81818182 = -16.406828689 x = -16.406828689 Simplifying x = -16.406828689Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.770465049, -16.406828689}
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