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Simplifying 2x2 + 20x + -2 = 0 Reorder the terms: -2 + 20x + 2x2 = 0 Solving -2 + 20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 10x + x2)' equal to zero and attempt to solve: Simplifying -1 + 10x + x2 = 0 Solving -1 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 10x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 10x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 10x + x2 = 0 + 1 10x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 10x + x2 = 1 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 = 1 + 25 Reorder the terms: 25 + 10x + x2 = 1 + 25 Combine like terms: 1 + 25 = 26 25 + 10x + x2 = 26 Factor a perfect square on the left side: (x + 5)(x + 5) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 5) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 5 = 5.099019514 Simplifying x + 5 = 5.099019514 Reorder the terms: 5 + x = 5.099019514 Solving 5 + x = 5.099019514 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 = 5.099019514 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.099019514 + -5 x = 5.099019514 + -5 Combine like terms: 5.099019514 + -5 = 0.099019514 x = 0.099019514 Simplifying x = 0.099019514Subproblem 2
x + 5 = -5.099019514 Simplifying x + 5 = -5.099019514 Reorder the terms: 5 + x = -5.099019514 Solving 5 + x = -5.099019514 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 = -5.099019514 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.099019514 + -5 x = -5.099019514 + -5 Combine like terms: -5.099019514 + -5 = -10.099019514 x = -10.099019514 Simplifying x = -10.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.099019514, -10.099019514}Solution
x = {0.099019514, -10.099019514}
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