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Simplifying 2x2 + -20x = 10 Reorder the terms: -20x + 2x2 = 10 Solving -20x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -20x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -10x + x2)' equal to zero and attempt to solve: Simplifying -5 + -10x + x2 = 0 Solving -5 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -10x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -10x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -10x + x2 = 0 + 5 -10x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -10x + x2 = 5 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 = 5 + 25 Reorder the terms: 25 + -10x + x2 = 5 + 25 Combine like terms: 5 + 25 = 30 25 + -10x + x2 = 30 Factor a perfect square on the left side: (x + -5)(x + -5) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + -5) equal to 5.477225575 and -5.477225575.Subproblem 1
x + -5 = 5.477225575 Simplifying x + -5 = 5.477225575 Reorder the terms: -5 + x = 5.477225575 Solving -5 + x = 5.477225575 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 = 5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.477225575 + 5 x = 5.477225575 + 5 Combine like terms: 5.477225575 + 5 = 10.477225575 x = 10.477225575 Simplifying x = 10.477225575Subproblem 2
x + -5 = -5.477225575 Simplifying x + -5 = -5.477225575 Reorder the terms: -5 + x = -5.477225575 Solving -5 + x = -5.477225575 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 = -5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.477225575 + 5 x = -5.477225575 + 5 Combine like terms: -5.477225575 + 5 = -0.477225575 x = -0.477225575 Simplifying x = -0.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.477225575, -0.477225575}Solution
x = {10.477225575, -0.477225575}
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