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Simplifying 5x2 + 29x + 6 = 0 Reorder the terms: 6 + 29x + 5x2 = 0 Solving 6 + 29x + 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'. 1.2 + 5.8x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 5.8x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 5.8x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 5.8x + x2 = 0 + -1.2 5.8x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 5.8x + x2 = -1.2 The x term is 5.8x. Take half its coefficient (2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. 5.8x + 8.41 + x2 = -1.2 + 8.41 Reorder the terms: 8.41 + 5.8x + x2 = -1.2 + 8.41 Combine like terms: -1.2 + 8.41 = 7.21 8.41 + 5.8x + x2 = 7.21 Factor a perfect square on the left side: (x + 2.9)(x + 2.9) = 7.21 Calculate the square root of the right side: 2.685144316 Break this problem into two subproblems by setting (x + 2.9) equal to 2.685144316 and -2.685144316.Subproblem 1
x + 2.9 = 2.685144316 Simplifying x + 2.9 = 2.685144316 Reorder the terms: 2.9 + x = 2.685144316 Solving 2.9 + x = 2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + x = 2.685144316 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + x = 2.685144316 + -2.9 x = 2.685144316 + -2.9 Combine like terms: 2.685144316 + -2.9 = -0.214855684 x = -0.214855684 Simplifying x = -0.214855684Subproblem 2
x + 2.9 = -2.685144316 Simplifying x + 2.9 = -2.685144316 Reorder the terms: 2.9 + x = -2.685144316 Solving 2.9 + x = -2.685144316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + x = -2.685144316 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + x = -2.685144316 + -2.9 x = -2.685144316 + -2.9 Combine like terms: -2.685144316 + -2.9 = -5.585144316 x = -5.585144316 Simplifying x = -5.585144316Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.214855684, -5.585144316}
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