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Simplifying 8x2 + 21 = -58x Reorder the terms: 21 + 8x2 = -58x Solving 21 + 8x2 = -58x Solving for variable 'x'. Reorder the terms: 21 + 58x + 8x2 = -58x + 58x Combine like terms: -58x + 58x = 0 21 + 58x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.625 + 7.25x + x2 = 0 Move the constant term to the right: Add '-2.625' to each side of the equation. 2.625 + 7.25x + -2.625 + x2 = 0 + -2.625 Reorder the terms: 2.625 + -2.625 + 7.25x + x2 = 0 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + 7.25x + x2 = 0 + -2.625 7.25x + x2 = 0 + -2.625 Combine like terms: 0 + -2.625 = -2.625 7.25x + x2 = -2.625 The x term is 7.25x. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25x + 13.140625 + x2 = -2.625 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = -2.625 + 13.140625 Combine like terms: -2.625 + 13.140625 = 10.515625 13.140625 + 7.25x + x2 = 10.515625 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = 10.515625 Calculate the square root of the right side: 3.242780443 Break this problem into two subproblems by setting (x + 3.625) equal to 3.242780443 and -3.242780443.Subproblem 1
x + 3.625 = 3.242780443 Simplifying x + 3.625 = 3.242780443 Reorder the terms: 3.625 + x = 3.242780443 Solving 3.625 + x = 3.242780443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = 3.242780443 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = 3.242780443 + -3.625 x = 3.242780443 + -3.625 Combine like terms: 3.242780443 + -3.625 = -0.382219557 x = -0.382219557 Simplifying x = -0.382219557Subproblem 2
x + 3.625 = -3.242780443 Simplifying x + 3.625 = -3.242780443 Reorder the terms: 3.625 + x = -3.242780443 Solving 3.625 + x = -3.242780443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = -3.242780443 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = -3.242780443 + -3.625 x = -3.242780443 + -3.625 Combine like terms: -3.242780443 + -3.625 = -6.867780443 x = -6.867780443 Simplifying x = -6.867780443Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.382219557, -6.867780443}
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