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Simplifying 0.9389x2 + 191.36x + -147195.52 = 0 Reorder the terms: -147195.52 + 191.36x + 0.9389x2 = 0 Solving -147195.52 + 191.36x + 0.9389x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.9389 the coefficient of the squared term: Divide each side by '0.9389'. -156774.4382 + 203.8129726x + x2 = 0 Move the constant term to the right: Add '156774.4382' to each side of the equation. -156774.4382 + 203.8129726x + 156774.4382 + x2 = 0 + 156774.4382 Reorder the terms: -156774.4382 + 156774.4382 + 203.8129726x + x2 = 0 + 156774.4382 Combine like terms: -156774.4382 + 156774.4382 = 0.0000 0.0000 + 203.8129726x + x2 = 0 + 156774.4382 203.8129726x + x2 = 0 + 156774.4382 Combine like terms: 0 + 156774.4382 = 156774.4382 203.8129726x + x2 = 156774.4382 The x term is 203.8129726x. Take half its coefficient (101.9064863). Square it (10384.93195) and add it to both sides. Add '10384.93195' to each side of the equation. 203.8129726x + 10384.93195 + x2 = 156774.4382 + 10384.93195 Reorder the terms: 10384.93195 + 203.8129726x + x2 = 156774.4382 + 10384.93195 Combine like terms: 156774.4382 + 10384.93195 = 167159.37015 10384.93195 + 203.8129726x + x2 = 167159.37015 Factor a perfect square on the left side: (x + 101.9064863)(x + 101.9064863) = 167159.37015 Calculate the square root of the right side: 408.851281214 Break this problem into two subproblems by setting (x + 101.9064863) equal to 408.851281214 and -408.851281214.Subproblem 1
x + 101.9064863 = 408.851281214 Simplifying x + 101.9064863 = 408.851281214 Reorder the terms: 101.9064863 + x = 408.851281214 Solving 101.9064863 + x = 408.851281214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-101.9064863' to each side of the equation. 101.9064863 + -101.9064863 + x = 408.851281214 + -101.9064863 Combine like terms: 101.9064863 + -101.9064863 = 0.0000000 0.0000000 + x = 408.851281214 + -101.9064863 x = 408.851281214 + -101.9064863 Combine like terms: 408.851281214 + -101.9064863 = 306.944794914 x = 306.944794914 Simplifying x = 306.944794914Subproblem 2
x + 101.9064863 = -408.851281214 Simplifying x + 101.9064863 = -408.851281214 Reorder the terms: 101.9064863 + x = -408.851281214 Solving 101.9064863 + x = -408.851281214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-101.9064863' to each side of the equation. 101.9064863 + -101.9064863 + x = -408.851281214 + -101.9064863 Combine like terms: 101.9064863 + -101.9064863 = 0.0000000 0.0000000 + x = -408.851281214 + -101.9064863 x = -408.851281214 + -101.9064863 Combine like terms: -408.851281214 + -101.9064863 = -510.757767514 x = -510.757767514 Simplifying x = -510.757767514Solution
The solution to the problem is based on the solutions from the subproblems. x = {306.944794914, -510.757767514}
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