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Simplifying 8x2 + 57x + 42 = 0 Reorder the terms: 42 + 57x + 8x2 = 0 Solving 42 + 57x + 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 + 7.125x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + 7.125x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + 7.125x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + 7.125x + x2 = 0 + -5.25 7.125x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 7.125x + x2 = -5.25 The x term is 7.125x. Take half its coefficient (3.5625). Square it (12.69140625) and add it to both sides. Add '12.69140625' to each side of the equation. 7.125x + 12.69140625 + x2 = -5.25 + 12.69140625 Reorder the terms: 12.69140625 + 7.125x + x2 = -5.25 + 12.69140625 Combine like terms: -5.25 + 12.69140625 = 7.44140625 12.69140625 + 7.125x + x2 = 7.44140625 Factor a perfect square on the left side: (x + 3.5625)(x + 3.5625) = 7.44140625 Calculate the square root of the right side: 2.727894105 Break this problem into two subproblems by setting (x + 3.5625) equal to 2.727894105 and -2.727894105.Subproblem 1
x + 3.5625 = 2.727894105 Simplifying x + 3.5625 = 2.727894105 Reorder the terms: 3.5625 + x = 2.727894105 Solving 3.5625 + x = 2.727894105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5625' to each side of the equation. 3.5625 + -3.5625 + x = 2.727894105 + -3.5625 Combine like terms: 3.5625 + -3.5625 = 0.0000 0.0000 + x = 2.727894105 + -3.5625 x = 2.727894105 + -3.5625 Combine like terms: 2.727894105 + -3.5625 = -0.834605895 x = -0.834605895 Simplifying x = -0.834605895Subproblem 2
x + 3.5625 = -2.727894105 Simplifying x + 3.5625 = -2.727894105 Reorder the terms: 3.5625 + x = -2.727894105 Solving 3.5625 + x = -2.727894105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5625' to each side of the equation. 3.5625 + -3.5625 + x = -2.727894105 + -3.5625 Combine like terms: 3.5625 + -3.5625 = 0.0000 0.0000 + x = -2.727894105 + -3.5625 x = -2.727894105 + -3.5625 Combine like terms: -2.727894105 + -3.5625 = -6.290394105 x = -6.290394105 Simplifying x = -6.290394105Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.834605895, -6.290394105}
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