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Simplifying 10x2 + 31x + 5 = 0 Reorder the terms: 5 + 31x + 10x2 = 0 Solving 5 + 31x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.5 + 3.1x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 3.1x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 3.1x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 3.1x + x2 = 0 + -0.5 3.1x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 3.1x + x2 = -0.5 The x term is 3.1x. Take half its coefficient (1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. 3.1x + 2.4025 + x2 = -0.5 + 2.4025 Reorder the terms: 2.4025 + 3.1x + x2 = -0.5 + 2.4025 Combine like terms: -0.5 + 2.4025 = 1.9025 2.4025 + 3.1x + x2 = 1.9025 Factor a perfect square on the left side: (x + 1.55)(x + 1.55) = 1.9025 Calculate the square root of the right side: 1.379311422 Break this problem into two subproblems by setting (x + 1.55) equal to 1.379311422 and -1.379311422.Subproblem 1
x + 1.55 = 1.379311422 Simplifying x + 1.55 = 1.379311422 Reorder the terms: 1.55 + x = 1.379311422 Solving 1.55 + x = 1.379311422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.55' to each side of the equation. 1.55 + -1.55 + x = 1.379311422 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + x = 1.379311422 + -1.55 x = 1.379311422 + -1.55 Combine like terms: 1.379311422 + -1.55 = -0.170688578 x = -0.170688578 Simplifying x = -0.170688578Subproblem 2
x + 1.55 = -1.379311422 Simplifying x + 1.55 = -1.379311422 Reorder the terms: 1.55 + x = -1.379311422 Solving 1.55 + x = -1.379311422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.55' to each side of the equation. 1.55 + -1.55 + x = -1.379311422 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + x = -1.379311422 + -1.55 x = -1.379311422 + -1.55 Combine like terms: -1.379311422 + -1.55 = -2.929311422 x = -2.929311422 Simplifying x = -2.929311422Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.170688578, -2.929311422}
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