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Simplifying -2x4 + 40x2 + 100 = 0 Reorder the terms: 100 + 40x2 + -2x4 = 0 Solving 100 + 40x2 + -2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + 20x2 + -1x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + 20x2 + -1x4)' equal to zero and attempt to solve: Simplifying 50 + 20x2 + -1x4 = 0 Solving 50 + 20x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -20x2 + x4 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -20x2 + 50 + x4 = 0 + 50 Reorder the terms: -50 + 50 + -20x2 + x4 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -20x2 + x4 = 0 + 50 -20x2 + x4 = 0 + 50 Combine like terms: 0 + 50 = 50 -20x2 + x4 = 50 The x term is -20x2. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x2 + 100 + x4 = 50 + 100 Reorder the terms: 100 + -20x2 + x4 = 50 + 100 Combine like terms: 50 + 100 = 150 100 + -20x2 + x4 = 150 Factor a perfect square on the left side: (x2 + -10)(x2 + -10) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (x2 + -10) equal to 12.247448714 and -12.247448714.Subproblem 1
x2 + -10 = 12.247448714 Simplifying x2 + -10 = 12.247448714 Reorder the terms: -10 + x2 = 12.247448714 Solving -10 + x2 = 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 + x2 = 12.247448714 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = 12.247448714 + 10 x2 = 12.247448714 + 10 Combine like terms: 12.247448714 + 10 = 22.247448714 x2 = 22.247448714 Simplifying x2 = 22.247448714 Take the square root of each side: x = {-4.716720123, 4.716720123}Subproblem 2
x2 + -10 = -12.247448714 Simplifying x2 + -10 = -12.247448714 Reorder the terms: -10 + x2 = -12.247448714 Solving -10 + x2 = -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 + x2 = -12.247448714 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = -12.247448714 + 10 x2 = -12.247448714 + 10 Combine like terms: -12.247448714 + 10 = -2.247448714 x2 = -2.247448714 Simplifying x2 = -2.247448714 Reorder the terms: 2.247448714 + x2 = -2.247448714 + 2.247448714 Combine like terms: -2.247448714 + 2.247448714 = 0.000000000 2.247448714 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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