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Simplifying 0.666x2 + 2.333x + -5 = 0 Reorder the terms: -5 + 2.333x + 0.666x2 = 0 Solving -5 + 2.333x + 0.666x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.666 the coefficient of the squared term: Divide each side by '0.666'. -7.507507508 + 3.503003003x + x2 = 0 Move the constant term to the right: Add '7.507507508' to each side of the equation. -7.507507508 + 3.503003003x + 7.507507508 + x2 = 0 + 7.507507508 Reorder the terms: -7.507507508 + 7.507507508 + 3.503003003x + x2 = 0 + 7.507507508 Combine like terms: -7.507507508 + 7.507507508 = 0.000000000 0.000000000 + 3.503003003x + x2 = 0 + 7.507507508 3.503003003x + x2 = 0 + 7.507507508 Combine like terms: 0 + 7.507507508 = 7.507507508 3.503003003x + x2 = 7.507507508 The x term is 3.503003003x. Take half its coefficient (1.751501502). Square it (3.067757512) and add it to both sides. Add '3.067757512' to each side of the equation. 3.503003003x + 3.067757512 + x2 = 7.507507508 + 3.067757512 Reorder the terms: 3.067757512 + 3.503003003x + x2 = 7.507507508 + 3.067757512 Combine like terms: 7.507507508 + 3.067757512 = 10.57526502 3.067757512 + 3.503003003x + x2 = 10.57526502 Factor a perfect square on the left side: (x + 1.751501502)(x + 1.751501502) = 10.57526502 Calculate the square root of the right side: 3.251963256 Break this problem into two subproblems by setting (x + 1.751501502) equal to 3.251963256 and -3.251963256.Subproblem 1
x + 1.751501502 = 3.251963256 Simplifying x + 1.751501502 = 3.251963256 Reorder the terms: 1.751501502 + x = 3.251963256 Solving 1.751501502 + x = 3.251963256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.751501502' to each side of the equation. 1.751501502 + -1.751501502 + x = 3.251963256 + -1.751501502 Combine like terms: 1.751501502 + -1.751501502 = 0.000000000 0.000000000 + x = 3.251963256 + -1.751501502 x = 3.251963256 + -1.751501502 Combine like terms: 3.251963256 + -1.751501502 = 1.500461754 x = 1.500461754 Simplifying x = 1.500461754Subproblem 2
x + 1.751501502 = -3.251963256 Simplifying x + 1.751501502 = -3.251963256 Reorder the terms: 1.751501502 + x = -3.251963256 Solving 1.751501502 + x = -3.251963256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.751501502' to each side of the equation. 1.751501502 + -1.751501502 + x = -3.251963256 + -1.751501502 Combine like terms: 1.751501502 + -1.751501502 = 0.000000000 0.000000000 + x = -3.251963256 + -1.751501502 x = -3.251963256 + -1.751501502 Combine like terms: -3.251963256 + -1.751501502 = -5.003464758 x = -5.003464758 Simplifying x = -5.003464758Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.500461754, -5.003464758}
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