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Simplifying 4X2 + -20X = 100 Reorder the terms: -20X + 4X2 = 100 Solving -20X + 4X2 = 100 Solving for variable 'X'. Reorder the terms: -100 + -20X + 4X2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -20X + 4X2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -5X + X2) = 0 Ignore the factor 4.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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