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Simplifying 20x2 + 127x + 33 = 0 Reorder the terms: 33 + 127x + 20x2 = 0 Solving 33 + 127x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1.65 + 6.35x + x2 = 0 Move the constant term to the right: Add '-1.65' to each side of the equation. 1.65 + 6.35x + -1.65 + x2 = 0 + -1.65 Reorder the terms: 1.65 + -1.65 + 6.35x + x2 = 0 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + 6.35x + x2 = 0 + -1.65 6.35x + x2 = 0 + -1.65 Combine like terms: 0 + -1.65 = -1.65 6.35x + x2 = -1.65 The x term is 6.35x. Take half its coefficient (3.175). Square it (10.080625) and add it to both sides. Add '10.080625' to each side of the equation. 6.35x + 10.080625 + x2 = -1.65 + 10.080625 Reorder the terms: 10.080625 + 6.35x + x2 = -1.65 + 10.080625 Combine like terms: -1.65 + 10.080625 = 8.430625 10.080625 + 6.35x + x2 = 8.430625 Factor a perfect square on the left side: (x + 3.175)(x + 3.175) = 8.430625 Calculate the square root of the right side: 2.903553857 Break this problem into two subproblems by setting (x + 3.175) equal to 2.903553857 and -2.903553857.Subproblem 1
x + 3.175 = 2.903553857 Simplifying x + 3.175 = 2.903553857 Reorder the terms: 3.175 + x = 2.903553857 Solving 3.175 + x = 2.903553857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.175' to each side of the equation. 3.175 + -3.175 + x = 2.903553857 + -3.175 Combine like terms: 3.175 + -3.175 = 0.000 0.000 + x = 2.903553857 + -3.175 x = 2.903553857 + -3.175 Combine like terms: 2.903553857 + -3.175 = -0.271446143 x = -0.271446143 Simplifying x = -0.271446143Subproblem 2
x + 3.175 = -2.903553857 Simplifying x + 3.175 = -2.903553857 Reorder the terms: 3.175 + x = -2.903553857 Solving 3.175 + x = -2.903553857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.175' to each side of the equation. 3.175 + -3.175 + x = -2.903553857 + -3.175 Combine like terms: 3.175 + -3.175 = 0.000 0.000 + x = -2.903553857 + -3.175 x = -2.903553857 + -3.175 Combine like terms: -2.903553857 + -3.175 = -6.078553857 x = -6.078553857 Simplifying x = -6.078553857Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.271446143, -6.078553857}
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