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Simplifying 2X2 + 40X = 100 Reorder the terms: 40X + 2X2 = 100 Solving 40X + 2X2 = 100 Solving for variable 'X'. Reorder the terms: -100 + 40X + 2X2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 40X + 2X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 20X + X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 20X + X2)' equal to zero and attempt to solve: Simplifying -50 + 20X + X2 = 0 Solving -50 + 20X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 20X + 50 + X2 = 0 + 50 Reorder the terms: -50 + 50 + 20X + X2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 20X + X2 = 0 + 50 20X + X2 = 0 + 50 Combine like terms: 0 + 50 = 50 20X + X2 = 50 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 = 50 + 100 Reorder the terms: 100 + 20X + X2 = 50 + 100 Combine like terms: 50 + 100 = 150 100 + 20X + X2 = 150 Factor a perfect square on the left side: (X + 10)(X + 10) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (X + 10) equal to 12.247448714 and -12.247448714.Subproblem 1
X + 10 = 12.247448714 Simplifying X + 10 = 12.247448714 Reorder the terms: 10 + X = 12.247448714 Solving 10 + X = 12.247448714 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 = 12.247448714 + -10 Combine like terms: 10 + -10 = 0 0 + X = 12.247448714 + -10 X = 12.247448714 + -10 Combine like terms: 12.247448714 + -10 = 2.247448714 X = 2.247448714 Simplifying X = 2.247448714Subproblem 2
X + 10 = -12.247448714 Simplifying X + 10 = -12.247448714 Reorder the terms: 10 + X = -12.247448714 Solving 10 + X = -12.247448714 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 = -12.247448714 + -10 Combine like terms: 10 + -10 = 0 0 + X = -12.247448714 + -10 X = -12.247448714 + -10 Combine like terms: -12.247448714 + -10 = -22.247448714 X = -22.247448714 Simplifying X = -22.247448714Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.247448714, -22.247448714}Solution
X = {2.247448714, -22.247448714}
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