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Simplifying 1.6x2 + 8.2x + 1 = 0 Reorder the terms: 1 + 8.2x + 1.6x2 = 0 Solving 1 + 8.2x + 1.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.6 the coefficient of the squared term: Divide each side by '1.6'. 0.625 + 5.125x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 5.125x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 5.125x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 5.125x + x2 = 0 + -0.625 5.125x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 5.125x + x2 = -0.625 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 = -0.625 + 6.56640625 Reorder the terms: 6.56640625 + 5.125x + x2 = -0.625 + 6.56640625 Combine like terms: -0.625 + 6.56640625 = 5.94140625 6.56640625 + 5.125x + x2 = 5.94140625 Factor a perfect square on the left side: (x + 2.5625)(x + 2.5625) = 5.94140625 Calculate the square root of the right side: 2.4375 Break this problem into two subproblems by setting (x + 2.5625) equal to 2.4375 and -2.4375.Subproblem 1
x + 2.5625 = 2.4375 Simplifying x + 2.5625 = 2.4375 Reorder the terms: 2.5625 + x = 2.4375 Solving 2.5625 + x = 2.4375 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 = 2.4375 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + x = 2.4375 + -2.5625 x = 2.4375 + -2.5625 Combine like terms: 2.4375 + -2.5625 = -0.125 x = -0.125 Simplifying x = -0.125Subproblem 2
x + 2.5625 = -2.4375 Simplifying x + 2.5625 = -2.4375 Reorder the terms: 2.5625 + x = -2.4375 Solving 2.5625 + x = -2.4375 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 = -2.4375 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + x = -2.4375 + -2.5625 x = -2.4375 + -2.5625 Combine like terms: -2.4375 + -2.5625 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.125, -5}
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