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Simplifying 8x2 + 41x + 42 = 0 Reorder the terms: 42 + 41x + 8x2 = 0 Solving 42 + 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'. 5.25 + 5.125x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + 5.125x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + 5.125x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + 5.125x + x2 = 0 + -5.25 5.125x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 5.125x + x2 = -5.25 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 = -5.25 + 6.56640625 Reorder the terms: 6.56640625 + 5.125x + x2 = -5.25 + 6.56640625 Combine like terms: -5.25 + 6.56640625 = 1.31640625 6.56640625 + 5.125x + x2 = 1.31640625 Factor a perfect square on the left side: (x + 2.5625)(x + 2.5625) = 1.31640625 Calculate the square root of the right side: 1.147347484 Break this problem into two subproblems by setting (x + 2.5625) equal to 1.147347484 and -1.147347484.Subproblem 1
x + 2.5625 = 1.147347484 Simplifying x + 2.5625 = 1.147347484 Reorder the terms: 2.5625 + x = 1.147347484 Solving 2.5625 + x = 1.147347484 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 = 1.147347484 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + x = 1.147347484 + -2.5625 x = 1.147347484 + -2.5625 Combine like terms: 1.147347484 + -2.5625 = -1.415152516 x = -1.415152516 Simplifying x = -1.415152516Subproblem 2
x + 2.5625 = -1.147347484 Simplifying x + 2.5625 = -1.147347484 Reorder the terms: 2.5625 + x = -1.147347484 Solving 2.5625 + x = -1.147347484 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 = -1.147347484 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + x = -1.147347484 + -2.5625 x = -1.147347484 + -2.5625 Combine like terms: -1.147347484 + -2.5625 = -3.709847484 x = -3.709847484 Simplifying x = -3.709847484Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.415152516, -3.709847484}
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