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Simplifying 2x2 + -10x = 50 Reorder the terms: -10x + 2x2 = 50 Solving -10x + 2x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + -10x + 2x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -5x + x2)' equal to zero and attempt to solve: Simplifying -25 + -5x + x2 = 0 Solving -25 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -5x + x2 = 0 + 25 -5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -5x + x2 = 25 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 25 + 6.25 Combine like terms: 25 + 6.25 = 31.25 6.25 + -5x + x2 = 31.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -2.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -2.5 = 5.590169944 Simplifying x + -2.5 = 5.590169944 Reorder the terms: -2.5 + x = 5.590169944 Solving -2.5 + x = 5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 5.590169944 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.590169944 + 2.5 x = 5.590169944 + 2.5 Combine like terms: 5.590169944 + 2.5 = 8.090169944 x = 8.090169944 Simplifying x = 8.090169944Subproblem 2
x + -2.5 = -5.590169944 Simplifying x + -2.5 = -5.590169944 Reorder the terms: -2.5 + x = -5.590169944 Solving -2.5 + x = -5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -5.590169944 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.590169944 + 2.5 x = -5.590169944 + 2.5 Combine like terms: -5.590169944 + 2.5 = -3.090169944 x = -3.090169944 Simplifying x = -3.090169944Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.090169944, -3.090169944}Solution
x = {8.090169944, -3.090169944}
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