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Simplifying 2x2 + -8x = 286 Reorder the terms: -8x + 2x2 = 286 Solving -8x + 2x2 = 286 Solving for variable 'x'. Reorder the terms: -286 + -8x + 2x2 = 286 + -286 Combine like terms: 286 + -286 = 0 -286 + -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-143 + -4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-143 + -4x + x2)' equal to zero and attempt to solve: Simplifying -143 + -4x + x2 = 0 Solving -143 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '143' to each side of the equation. -143 + -4x + 143 + x2 = 0 + 143 Reorder the terms: -143 + 143 + -4x + x2 = 0 + 143 Combine like terms: -143 + 143 = 0 0 + -4x + x2 = 0 + 143 -4x + x2 = 0 + 143 Combine like terms: 0 + 143 = 143 -4x + x2 = 143 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 143 + 4 Reorder the terms: 4 + -4x + x2 = 143 + 4 Combine like terms: 143 + 4 = 147 4 + -4x + x2 = 147 Factor a perfect square on the left side: (x + -2)(x + -2) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (x + -2) equal to 12.124355653 and -12.124355653.Subproblem 1
x + -2 = 12.124355653 Simplifying x + -2 = 12.124355653 Reorder the terms: -2 + x = 12.124355653 Solving -2 + x = 12.124355653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 12.124355653 + 2 Combine like terms: -2 + 2 = 0 0 + x = 12.124355653 + 2 x = 12.124355653 + 2 Combine like terms: 12.124355653 + 2 = 14.124355653 x = 14.124355653 Simplifying x = 14.124355653Subproblem 2
x + -2 = -12.124355653 Simplifying x + -2 = -12.124355653 Reorder the terms: -2 + x = -12.124355653 Solving -2 + x = -12.124355653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -12.124355653 + 2 Combine like terms: -2 + 2 = 0 0 + x = -12.124355653 + 2 x = -12.124355653 + 2 Combine like terms: -12.124355653 + 2 = -10.124355653 x = -10.124355653 Simplifying x = -10.124355653Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.124355653, -10.124355653}Solution
x = {14.124355653, -10.124355653}
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