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Simplifying 8x2 + 121x + -22 = 0 Reorder the terms: -22 + 121x + 8x2 = 0 Solving -22 + 121x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.75 + 15.125x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 15.125x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 15.125x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 15.125x + x2 = 0 + 2.75 15.125x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 15.125x + x2 = 2.75 The x term is 15.125x. Take half its coefficient (7.5625). Square it (57.19140625) and add it to both sides. Add '57.19140625' to each side of the equation. 15.125x + 57.19140625 + x2 = 2.75 + 57.19140625 Reorder the terms: 57.19140625 + 15.125x + x2 = 2.75 + 57.19140625 Combine like terms: 2.75 + 57.19140625 = 59.94140625 57.19140625 + 15.125x + x2 = 59.94140625 Factor a perfect square on the left side: (x + 7.5625)(x + 7.5625) = 59.94140625 Calculate the square root of the right side: 7.742183558 Break this problem into two subproblems by setting (x + 7.5625) equal to 7.742183558 and -7.742183558.Subproblem 1
x + 7.5625 = 7.742183558 Simplifying x + 7.5625 = 7.742183558 Reorder the terms: 7.5625 + x = 7.742183558 Solving 7.5625 + x = 7.742183558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5625' to each side of the equation. 7.5625 + -7.5625 + x = 7.742183558 + -7.5625 Combine like terms: 7.5625 + -7.5625 = 0.0000 0.0000 + x = 7.742183558 + -7.5625 x = 7.742183558 + -7.5625 Combine like terms: 7.742183558 + -7.5625 = 0.179683558 x = 0.179683558 Simplifying x = 0.179683558Subproblem 2
x + 7.5625 = -7.742183558 Simplifying x + 7.5625 = -7.742183558 Reorder the terms: 7.5625 + x = -7.742183558 Solving 7.5625 + x = -7.742183558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5625' to each side of the equation. 7.5625 + -7.5625 + x = -7.742183558 + -7.5625 Combine like terms: 7.5625 + -7.5625 = 0.0000 0.0000 + x = -7.742183558 + -7.5625 x = -7.742183558 + -7.5625 Combine like terms: -7.742183558 + -7.5625 = -15.304683558 x = -15.304683558 Simplifying x = -15.304683558Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.179683558, -15.304683558}
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