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Simplifying 2x2 + 62x + 33 = 0 Reorder the terms: 33 + 62x + 2x2 = 0 Solving 33 + 62x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 16.5 + 31x + x2 = 0 Move the constant term to the right: Add '-16.5' to each side of the equation. 16.5 + 31x + -16.5 + x2 = 0 + -16.5 Reorder the terms: 16.5 + -16.5 + 31x + x2 = 0 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + 31x + x2 = 0 + -16.5 31x + x2 = 0 + -16.5 Combine like terms: 0 + -16.5 = -16.5 31x + x2 = -16.5 The x term is 31x. Take half its coefficient (15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. 31x + 240.25 + x2 = -16.5 + 240.25 Reorder the terms: 240.25 + 31x + x2 = -16.5 + 240.25 Combine like terms: -16.5 + 240.25 = 223.75 240.25 + 31x + x2 = 223.75 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 223.75 Calculate the square root of the right side: 14.958275302 Break this problem into two subproblems by setting (x + 15.5) equal to 14.958275302 and -14.958275302.Subproblem 1
x + 15.5 = 14.958275302 Simplifying x + 15.5 = 14.958275302 Reorder the terms: 15.5 + x = 14.958275302 Solving 15.5 + x = 14.958275302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 14.958275302 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 14.958275302 + -15.5 x = 14.958275302 + -15.5 Combine like terms: 14.958275302 + -15.5 = -0.541724698 x = -0.541724698 Simplifying x = -0.541724698Subproblem 2
x + 15.5 = -14.958275302 Simplifying x + 15.5 = -14.958275302 Reorder the terms: 15.5 + x = -14.958275302 Solving 15.5 + x = -14.958275302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -14.958275302 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -14.958275302 + -15.5 x = -14.958275302 + -15.5 Combine like terms: -14.958275302 + -15.5 = -30.458275302 x = -30.458275302 Simplifying x = -30.458275302Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.541724698, -30.458275302}
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