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Simplifying 5x2 + 29x + 27 = 0 Reorder the terms: 27 + 29x + 5x2 = 0 Solving 27 + 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'. 5.4 + 5.8x + x2 = 0 Move the constant term to the right: Add '-5.4' to each side of the equation. 5.4 + 5.8x + -5.4 + x2 = 0 + -5.4 Reorder the terms: 5.4 + -5.4 + 5.8x + x2 = 0 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + 5.8x + x2 = 0 + -5.4 5.8x + x2 = 0 + -5.4 Combine like terms: 0 + -5.4 = -5.4 5.8x + x2 = -5.4 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 = -5.4 + 8.41 Reorder the terms: 8.41 + 5.8x + x2 = -5.4 + 8.41 Combine like terms: -5.4 + 8.41 = 3.01 8.41 + 5.8x + x2 = 3.01 Factor a perfect square on the left side: (x + 2.9)(x + 2.9) = 3.01 Calculate the square root of the right side: 1.734935157 Break this problem into two subproblems by setting (x + 2.9) equal to 1.734935157 and -1.734935157.Subproblem 1
x + 2.9 = 1.734935157 Simplifying x + 2.9 = 1.734935157 Reorder the terms: 2.9 + x = 1.734935157 Solving 2.9 + x = 1.734935157 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 = 1.734935157 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + x = 1.734935157 + -2.9 x = 1.734935157 + -2.9 Combine like terms: 1.734935157 + -2.9 = -1.165064843 x = -1.165064843 Simplifying x = -1.165064843Subproblem 2
x + 2.9 = -1.734935157 Simplifying x + 2.9 = -1.734935157 Reorder the terms: 2.9 + x = -1.734935157 Solving 2.9 + x = -1.734935157 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 = -1.734935157 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + x = -1.734935157 + -2.9 x = -1.734935157 + -2.9 Combine like terms: -1.734935157 + -2.9 = -4.634935157 x = -4.634935157 Simplifying x = -4.634935157Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.165064843, -4.634935157}
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