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Simplifying 5x2 + 9x + -32 = 0 Reorder the terms: -32 + 9x + 5x2 = 0 Solving -32 + 9x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.4 + 1.8x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + 1.8x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + 1.8x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + 1.8x + x2 = 0 + 6.4 1.8x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 1.8x + x2 = 6.4 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 6.4 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 6.4 + 0.81 Combine like terms: 6.4 + 0.81 = 7.21 0.81 + 1.8x + x2 = 7.21 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 7.21 Calculate the square root of the right side: 2.685144316 Break this problem into two subproblems by setting (x + 0.9) equal to 2.685144316 and -2.685144316.Subproblem 1
x + 0.9 = 2.685144316 Simplifying x + 0.9 = 2.685144316 Reorder the terms: 0.9 + x = 2.685144316 Solving 0.9 + x = 2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 2.685144316 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 2.685144316 + -0.9 x = 2.685144316 + -0.9 Combine like terms: 2.685144316 + -0.9 = 1.785144316 x = 1.785144316 Simplifying x = 1.785144316Subproblem 2
x + 0.9 = -2.685144316 Simplifying x + 0.9 = -2.685144316 Reorder the terms: 0.9 + x = -2.685144316 Solving 0.9 + x = -2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -2.685144316 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -2.685144316 + -0.9 x = -2.685144316 + -0.9 Combine like terms: -2.685144316 + -0.9 = -3.585144316 x = -3.585144316 Simplifying x = -3.585144316Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.785144316, -3.585144316}
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