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Simplifying 5x2 + 39x + 40 = 0 Reorder the terms: 40 + 39x + 5x2 = 0 Solving 40 + 39x + 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'. 8 + 7.8x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 7.8x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 7.8x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7.8x + x2 = 0 + -8 7.8x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 7.8x + x2 = -8 The x term is 7.8x. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8x + 15.21 + x2 = -8 + 15.21 Reorder the terms: 15.21 + 7.8x + x2 = -8 + 15.21 Combine like terms: -8 + 15.21 = 7.21 15.21 + 7.8x + x2 = 7.21 Factor a perfect square on the left side: (x + 3.9)(x + 3.9) = 7.21 Calculate the square root of the right side: 2.685144316 Break this problem into two subproblems by setting (x + 3.9) equal to 2.685144316 and -2.685144316.Subproblem 1
x + 3.9 = 2.685144316 Simplifying x + 3.9 = 2.685144316 Reorder the terms: 3.9 + x = 2.685144316 Solving 3.9 + x = 2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = 2.685144316 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = 2.685144316 + -3.9 x = 2.685144316 + -3.9 Combine like terms: 2.685144316 + -3.9 = -1.214855684 x = -1.214855684 Simplifying x = -1.214855684Subproblem 2
x + 3.9 = -2.685144316 Simplifying x + 3.9 = -2.685144316 Reorder the terms: 3.9 + x = -2.685144316 Solving 3.9 + x = -2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = -2.685144316 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = -2.685144316 + -3.9 x = -2.685144316 + -3.9 Combine like terms: -2.685144316 + -3.9 = -6.585144316 x = -6.585144316 Simplifying x = -6.585144316Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.214855684, -6.585144316}
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