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Simplifying 4x2 + -80x + 86 = 0 Reorder the terms: 86 + -80x + 4x2 = 0 Solving 86 + -80x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(43 + -40x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(43 + -40x + 2x2)' equal to zero and attempt to solve: Simplifying 43 + -40x + 2x2 = 0 Solving 43 + -40x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 21.5 + -20x + x2 = 0 Move the constant term to the right: Add '-21.5' to each side of the equation. 21.5 + -20x + -21.5 + x2 = 0 + -21.5 Reorder the terms: 21.5 + -21.5 + -20x + x2 = 0 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + -20x + x2 = 0 + -21.5 -20x + x2 = 0 + -21.5 Combine like terms: 0 + -21.5 = -21.5 -20x + x2 = -21.5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -21.5 + 100 Reorder the terms: 100 + -20x + x2 = -21.5 + 100 Combine like terms: -21.5 + 100 = 78.5 100 + -20x + x2 = 78.5 Factor a perfect square on the left side: (x + -10)(x + -10) = 78.5 Calculate the square root of the right side: 8.860022573 Break this problem into two subproblems by setting (x + -10) equal to 8.860022573 and -8.860022573.Subproblem 1
x + -10 = 8.860022573 Simplifying x + -10 = 8.860022573 Reorder the terms: -10 + x = 8.860022573 Solving -10 + x = 8.860022573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 8.860022573 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.860022573 + 10 x = 8.860022573 + 10 Combine like terms: 8.860022573 + 10 = 18.860022573 x = 18.860022573 Simplifying x = 18.860022573Subproblem 2
x + -10 = -8.860022573 Simplifying x + -10 = -8.860022573 Reorder the terms: -10 + x = -8.860022573 Solving -10 + x = -8.860022573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -8.860022573 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.860022573 + 10 x = -8.860022573 + 10 Combine like terms: -8.860022573 + 10 = 1.139977427 x = 1.139977427 Simplifying x = 1.139977427Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.860022573, 1.139977427}Solution
x = {18.860022573, 1.139977427}
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