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Simplifying 2x2 + -40x = 8 Reorder the terms: -40x + 2x2 = 8 Solving -40x + 2x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -40x + 2x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -40x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -20x + x2)' equal to zero and attempt to solve: Simplifying -4 + -20x + x2 = 0 Solving -4 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -20x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -20x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -20x + x2 = 0 + 4 -20x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -20x + x2 = 4 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 = 4 + 100 Reorder the terms: 100 + -20x + x2 = 4 + 100 Combine like terms: 4 + 100 = 104 100 + -20x + x2 = 104 Factor a perfect square on the left side: (x + -10)(x + -10) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (x + -10) equal to 10.198039027 and -10.198039027.Subproblem 1
x + -10 = 10.198039027 Simplifying x + -10 = 10.198039027 Reorder the terms: -10 + x = 10.198039027 Solving -10 + x = 10.198039027 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 = 10.198039027 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.198039027 + 10 x = 10.198039027 + 10 Combine like terms: 10.198039027 + 10 = 20.198039027 x = 20.198039027 Simplifying x = 20.198039027Subproblem 2
x + -10 = -10.198039027 Simplifying x + -10 = -10.198039027 Reorder the terms: -10 + x = -10.198039027 Solving -10 + x = -10.198039027 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 = -10.198039027 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.198039027 + 10 x = -10.198039027 + 10 Combine like terms: -10.198039027 + 10 = -0.198039027 x = -0.198039027 Simplifying x = -0.198039027Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.198039027, -0.198039027}Solution
x = {20.198039027, -0.198039027}
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