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Simplifying 80x2 + 122x + -80 = 0 Reorder the terms: -80 + 122x + 80x2 = 0 Solving -80 + 122x + 80x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + 61x + 40x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + 61x + 40x2)' equal to zero and attempt to solve: Simplifying -40 + 61x + 40x2 = 0 Solving -40 + 61x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -1 + 1.525x + x2 = 0.0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.525x + 1 + x2 = 0.0 + 1 Reorder the terms: -1 + 1 + 1.525x + x2 = 0.0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.525x + x2 = 0.0 + 1 1.525x + x2 = 0.0 + 1 Combine like terms: 0.0 + 1 = 1 1.525x + x2 = 1 The x term is 1.525x. Take half its coefficient (0.7625). Square it (0.58140625) and add it to both sides. Add '0.58140625' to each side of the equation. 1.525x + 0.58140625 + x2 = 1 + 0.58140625 Reorder the terms: 0.58140625 + 1.525x + x2 = 1 + 0.58140625 Combine like terms: 1 + 0.58140625 = 1.58140625 0.58140625 + 1.525x + x2 = 1.58140625 Factor a perfect square on the left side: (x + 0.7625)(x + 0.7625) = 1.58140625 Calculate the square root of the right side: 1.257539761 Break this problem into two subproblems by setting (x + 0.7625) equal to 1.257539761 and -1.257539761.Subproblem 1
x + 0.7625 = 1.257539761 Simplifying x + 0.7625 = 1.257539761 Reorder the terms: 0.7625 + x = 1.257539761 Solving 0.7625 + x = 1.257539761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7625' to each side of the equation. 0.7625 + -0.7625 + x = 1.257539761 + -0.7625 Combine like terms: 0.7625 + -0.7625 = 0.0000 0.0000 + x = 1.257539761 + -0.7625 x = 1.257539761 + -0.7625 Combine like terms: 1.257539761 + -0.7625 = 0.495039761 x = 0.495039761 Simplifying x = 0.495039761Subproblem 2
x + 0.7625 = -1.257539761 Simplifying x + 0.7625 = -1.257539761 Reorder the terms: 0.7625 + x = -1.257539761 Solving 0.7625 + x = -1.257539761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7625' to each side of the equation. 0.7625 + -0.7625 + x = -1.257539761 + -0.7625 Combine like terms: 0.7625 + -0.7625 = 0.0000 0.0000 + x = -1.257539761 + -0.7625 x = -1.257539761 + -0.7625 Combine like terms: -1.257539761 + -0.7625 = -2.020039761 x = -2.020039761 Simplifying x = -2.020039761Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.495039761, -2.020039761}Solution
x = {0.495039761, -2.020039761}
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