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Simplifying 8x2 + 25x + 2 = 0 Reorder the terms: 2 + 25x + 8x2 = 0 Solving 2 + 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'. 0.25 + 3.125x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 3.125x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 3.125x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 3.125x + x2 = 0 + -0.25 3.125x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 3.125x + x2 = -0.25 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 = -0.25 + 2.44140625 Reorder the terms: 2.44140625 + 3.125x + x2 = -0.25 + 2.44140625 Combine like terms: -0.25 + 2.44140625 = 2.19140625 2.44140625 + 3.125x + x2 = 2.19140625 Factor a perfect square on the left side: (x + 1.5625)(x + 1.5625) = 2.19140625 Calculate the square root of the right side: 1.48033991 Break this problem into two subproblems by setting (x + 1.5625) equal to 1.48033991 and -1.48033991.Subproblem 1
x + 1.5625 = 1.48033991 Simplifying x + 1.5625 = 1.48033991 Reorder the terms: 1.5625 + x = 1.48033991 Solving 1.5625 + x = 1.48033991 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 = 1.48033991 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 1.48033991 + -1.5625 x = 1.48033991 + -1.5625 Combine like terms: 1.48033991 + -1.5625 = -0.08216009 x = -0.08216009 Simplifying x = -0.08216009Subproblem 2
x + 1.5625 = -1.48033991 Simplifying x + 1.5625 = -1.48033991 Reorder the terms: 1.5625 + x = -1.48033991 Solving 1.5625 + x = -1.48033991 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 = -1.48033991 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -1.48033991 + -1.5625 x = -1.48033991 + -1.5625 Combine like terms: -1.48033991 + -1.5625 = -3.04283991 x = -3.04283991 Simplifying x = -3.04283991Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.08216009, -3.04283991}
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