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Simplifying 2x2 + 20x + -4 = 80 Reorder the terms: -4 + 20x + 2x2 = 80 Solving -4 + 20x + 2x2 = 80 Solving for variable 'x'. Reorder the terms: -4 + -80 + 20x + 2x2 = 80 + -80 Combine like terms: -4 + -80 = -84 -84 + 20x + 2x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -84 + 20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + 10x + x2)' equal to zero and attempt to solve: Simplifying -42 + 10x + x2 = 0 Solving -42 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 10x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 10x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 10x + x2 = 0 + 42 10x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 10x + x2 = 42 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 42 + 25 Reorder the terms: 25 + 10x + x2 = 42 + 25 Combine like terms: 42 + 25 = 67 25 + 10x + x2 = 67 Factor a perfect square on the left side: (x + 5)(x + 5) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 5) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 5 = 8.185352772 Simplifying x + 5 = 8.185352772 Reorder the terms: 5 + x = 8.185352772 Solving 5 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 8.185352772 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.185352772 + -5 x = 8.185352772 + -5 Combine like terms: 8.185352772 + -5 = 3.185352772 x = 3.185352772 Simplifying x = 3.185352772Subproblem 2
x + 5 = -8.185352772 Simplifying x + 5 = -8.185352772 Reorder the terms: 5 + x = -8.185352772 Solving 5 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -8.185352772 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.185352772 + -5 x = -8.185352772 + -5 Combine like terms: -8.185352772 + -5 = -13.185352772 x = -13.185352772 Simplifying x = -13.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.185352772, -13.185352772}Solution
x = {3.185352772, -13.185352772}
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