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Simplifying 0.5x2 + 9x + 3.2 = 0 Reorder the terms: 3.2 + 9x + 0.5x2 = 0 Solving 3.2 + 9x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 6.4 + 18x + x2 = 0 Move the constant term to the right: Add '-6.4' to each side of the equation. 6.4 + 18x + -6.4 + x2 = 0 + -6.4 Reorder the terms: 6.4 + -6.4 + 18x + x2 = 0 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + 18x + x2 = 0 + -6.4 18x + x2 = 0 + -6.4 Combine like terms: 0 + -6.4 = -6.4 18x + x2 = -6.4 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -6.4 + 81 Reorder the terms: 81 + 18x + x2 = -6.4 + 81 Combine like terms: -6.4 + 81 = 74.6 81 + 18x + x2 = 74.6 Factor a perfect square on the left side: (x + 9)(x + 9) = 74.6 Calculate the square root of the right side: 8.637129153 Break this problem into two subproblems by setting (x + 9) equal to 8.637129153 and -8.637129153.Subproblem 1
x + 9 = 8.637129153 Simplifying x + 9 = 8.637129153 Reorder the terms: 9 + x = 8.637129153 Solving 9 + x = 8.637129153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 8.637129153 + -9 Combine like terms: 9 + -9 = 0 0 + x = 8.637129153 + -9 x = 8.637129153 + -9 Combine like terms: 8.637129153 + -9 = -0.362870847 x = -0.362870847 Simplifying x = -0.362870847Subproblem 2
x + 9 = -8.637129153 Simplifying x + 9 = -8.637129153 Reorder the terms: 9 + x = -8.637129153 Solving 9 + x = -8.637129153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -8.637129153 + -9 Combine like terms: 9 + -9 = 0 0 + x = -8.637129153 + -9 x = -8.637129153 + -9 Combine like terms: -8.637129153 + -9 = -17.637129153 x = -17.637129153 Simplifying x = -17.637129153Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.362870847, -17.637129153}
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