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Simplifying -8x2 + -41x + 36 = 0 Reorder the terms: 36 + -41x + -8x2 = 0 Solving 36 + -41x + -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'. -4.5 + 5.125x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 5.125x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 5.125x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 5.125x + x2 = 0 + 4.5 5.125x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 5.125x + x2 = 4.5 The x term is 5.125x. Take half its coefficient (2.5625). Square it (6.56640625) and add it to both sides. Add '6.56640625' to each side of the equation. 5.125x + 6.56640625 + x2 = 4.5 + 6.56640625 Reorder the terms: 6.56640625 + 5.125x + x2 = 4.5 + 6.56640625 Combine like terms: 4.5 + 6.56640625 = 11.06640625 6.56640625 + 5.125x + x2 = 11.06640625 Factor a perfect square on the left side: (x + 2.5625)(x + 2.5625) = 11.06640625 Calculate the square root of the right side: 3.326620846 Break this problem into two subproblems by setting (x + 2.5625) equal to 3.326620846 and -3.326620846.Subproblem 1
x + 2.5625 = 3.326620846 Simplifying x + 2.5625 = 3.326620846 Reorder the terms: 2.5625 + x = 3.326620846 Solving 2.5625 + x = 3.326620846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5625' to each side of the equation. 2.5625 + -2.5625 + x = 3.326620846 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + x = 3.326620846 + -2.5625 x = 3.326620846 + -2.5625 Combine like terms: 3.326620846 + -2.5625 = 0.764120846 x = 0.764120846 Simplifying x = 0.764120846Subproblem 2
x + 2.5625 = -3.326620846 Simplifying x + 2.5625 = -3.326620846 Reorder the terms: 2.5625 + x = -3.326620846 Solving 2.5625 + x = -3.326620846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5625' to each side of the equation. 2.5625 + -2.5625 + x = -3.326620846 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + x = -3.326620846 + -2.5625 x = -3.326620846 + -2.5625 Combine like terms: -3.326620846 + -2.5625 = -5.889120846 x = -5.889120846 Simplifying x = -5.889120846Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.764120846, -5.889120846}
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