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Simplifying 158x2 + -23x + -8 = 0 Reorder the terms: -8 + -23x + 158x2 = 0 Solving -8 + -23x + 158x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 158 the coefficient of the squared term: Divide each side by '158'. -0.05063291139 + -0.1455696203x + x2 = 0 Move the constant term to the right: Add '0.05063291139' to each side of the equation. -0.05063291139 + -0.1455696203x + 0.05063291139 + x2 = 0 + 0.05063291139 Reorder the terms: -0.05063291139 + 0.05063291139 + -0.1455696203x + x2 = 0 + 0.05063291139 Combine like terms: -0.05063291139 + 0.05063291139 = 0.00000000000 0.00000000000 + -0.1455696203x + x2 = 0 + 0.05063291139 -0.1455696203x + x2 = 0 + 0.05063291139 Combine like terms: 0 + 0.05063291139 = 0.05063291139 -0.1455696203x + x2 = 0.05063291139 The x term is -0.1455696203x. Take half its coefficient (-0.07278481015). Square it (0.005297628589) and add it to both sides. Add '0.005297628589' to each side of the equation. -0.1455696203x + 0.005297628589 + x2 = 0.05063291139 + 0.005297628589 Reorder the terms: 0.005297628589 + -0.1455696203x + x2 = 0.05063291139 + 0.005297628589 Combine like terms: 0.05063291139 + 0.005297628589 = 0.055930539979 0.005297628589 + -0.1455696203x + x2 = 0.055930539979 Factor a perfect square on the left side: (x + -0.07278481015)(x + -0.07278481015) = 0.055930539979 Calculate the square root of the right side: 0.236496385 Break this problem into two subproblems by setting (x + -0.07278481015) equal to 0.236496385 and -0.236496385.Subproblem 1
x + -0.07278481015 = 0.236496385 Simplifying x + -0.07278481015 = 0.236496385 Reorder the terms: -0.07278481015 + x = 0.236496385 Solving -0.07278481015 + x = 0.236496385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07278481015' to each side of the equation. -0.07278481015 + 0.07278481015 + x = 0.236496385 + 0.07278481015 Combine like terms: -0.07278481015 + 0.07278481015 = 0.00000000000 0.00000000000 + x = 0.236496385 + 0.07278481015 x = 0.236496385 + 0.07278481015 Combine like terms: 0.236496385 + 0.07278481015 = 0.30928119515 x = 0.30928119515 Simplifying x = 0.30928119515Subproblem 2
x + -0.07278481015 = -0.236496385 Simplifying x + -0.07278481015 = -0.236496385 Reorder the terms: -0.07278481015 + x = -0.236496385 Solving -0.07278481015 + x = -0.236496385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07278481015' to each side of the equation. -0.07278481015 + 0.07278481015 + x = -0.236496385 + 0.07278481015 Combine like terms: -0.07278481015 + 0.07278481015 = 0.00000000000 0.00000000000 + x = -0.236496385 + 0.07278481015 x = -0.236496385 + 0.07278481015 Combine like terms: -0.236496385 + 0.07278481015 = -0.16371157485 x = -0.16371157485 Simplifying x = -0.16371157485Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.30928119515, -0.16371157485}
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