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Simplifying 5x2 + 46x + 40 = 0 Reorder the terms: 40 + 46x + 5x2 = 0 Solving 40 + 46x + 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 + 9.2x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 9.2x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 9.2x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 9.2x + x2 = 0 + -8 9.2x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 9.2x + x2 = -8 The x term is 9.2x. Take half its coefficient (4.6). Square it (21.16) and add it to both sides. Add '21.16' to each side of the equation. 9.2x + 21.16 + x2 = -8 + 21.16 Reorder the terms: 21.16 + 9.2x + x2 = -8 + 21.16 Combine like terms: -8 + 21.16 = 13.16 21.16 + 9.2x + x2 = 13.16 Factor a perfect square on the left side: (x + 4.6)(x + 4.6) = 13.16 Calculate the square root of the right side: 3.627671429 Break this problem into two subproblems by setting (x + 4.6) equal to 3.627671429 and -3.627671429.Subproblem 1
x + 4.6 = 3.627671429 Simplifying x + 4.6 = 3.627671429 Reorder the terms: 4.6 + x = 3.627671429 Solving 4.6 + x = 3.627671429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6' to each side of the equation. 4.6 + -4.6 + x = 3.627671429 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + x = 3.627671429 + -4.6 x = 3.627671429 + -4.6 Combine like terms: 3.627671429 + -4.6 = -0.972328571 x = -0.972328571 Simplifying x = -0.972328571Subproblem 2
x + 4.6 = -3.627671429 Simplifying x + 4.6 = -3.627671429 Reorder the terms: 4.6 + x = -3.627671429 Solving 4.6 + x = -3.627671429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6' to each side of the equation. 4.6 + -4.6 + x = -3.627671429 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + x = -3.627671429 + -4.6 x = -3.627671429 + -4.6 Combine like terms: -3.627671429 + -4.6 = -8.227671429 x = -8.227671429 Simplifying x = -8.227671429Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.972328571, -8.227671429}
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