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Simplifying 8x2 + 25x + 19 = 0 Reorder the terms: 19 + 25x + 8x2 = 0 Solving 19 + 25x + 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'. 2.375 + 3.125x + x2 = 0 Move the constant term to the right: Add '-2.375' to each side of the equation. 2.375 + 3.125x + -2.375 + x2 = 0 + -2.375 Reorder the terms: 2.375 + -2.375 + 3.125x + x2 = 0 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + 3.125x + x2 = 0 + -2.375 3.125x + x2 = 0 + -2.375 Combine like terms: 0 + -2.375 = -2.375 3.125x + x2 = -2.375 The x term is 3.125x. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125x + 2.44140625 + x2 = -2.375 + 2.44140625 Reorder the terms: 2.44140625 + 3.125x + x2 = -2.375 + 2.44140625 Combine like terms: -2.375 + 2.44140625 = 0.06640625 2.44140625 + 3.125x + x2 = 0.06640625 Factor a perfect square on the left side: (x + 1.5625)(x + 1.5625) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (x + 1.5625) equal to 0.257694102 and -0.257694102.Subproblem 1
x + 1.5625 = 0.257694102 Simplifying x + 1.5625 = 0.257694102 Reorder the terms: 1.5625 + x = 0.257694102 Solving 1.5625 + x = 0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = 0.257694102 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 0.257694102 + -1.5625 x = 0.257694102 + -1.5625 Combine like terms: 0.257694102 + -1.5625 = -1.304805898 x = -1.304805898 Simplifying x = -1.304805898Subproblem 2
x + 1.5625 = -0.257694102 Simplifying x + 1.5625 = -0.257694102 Reorder the terms: 1.5625 + x = -0.257694102 Solving 1.5625 + x = -0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = -0.257694102 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -0.257694102 + -1.5625 x = -0.257694102 + -1.5625 Combine like terms: -0.257694102 + -1.5625 = -1.820194102 x = -1.820194102 Simplifying x = -1.820194102Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.304805898, -1.820194102}
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