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Simplifying 12x4 + -480x2 + -4500 = 0 Reorder the terms: -4500 + -480x2 + 12x4 = 0 Solving -4500 + -480x2 + 12x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-375 + -40x2 + x4) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-375 + -40x2 + x4)' equal to zero and attempt to solve: Simplifying -375 + -40x2 + x4 = 0 Solving -375 + -40x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '375' to each side of the equation. -375 + -40x2 + 375 + x4 = 0 + 375 Reorder the terms: -375 + 375 + -40x2 + x4 = 0 + 375 Combine like terms: -375 + 375 = 0 0 + -40x2 + x4 = 0 + 375 -40x2 + x4 = 0 + 375 Combine like terms: 0 + 375 = 375 -40x2 + x4 = 375 The x term is -40x2. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x2 + 400 + x4 = 375 + 400 Reorder the terms: 400 + -40x2 + x4 = 375 + 400 Combine like terms: 375 + 400 = 775 400 + -40x2 + x4 = 775 Factor a perfect square on the left side: (x2 + -20)(x2 + -20) = 775 Calculate the square root of the right side: 27.838821814 Break this problem into two subproblems by setting (x2 + -20) equal to 27.838821814 and -27.838821814.Subproblem 1
x2 + -20 = 27.838821814 Simplifying x2 + -20 = 27.838821814 Reorder the terms: -20 + x2 = 27.838821814 Solving -20 + x2 = 27.838821814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x2 = 27.838821814 + 20 Combine like terms: -20 + 20 = 0 0 + x2 = 27.838821814 + 20 x2 = 27.838821814 + 20 Combine like terms: 27.838821814 + 20 = 47.838821814 x2 = 47.838821814 Simplifying x2 = 47.838821814 Take the square root of each side: x = {-6.916561415, 6.916561415}Subproblem 2
x2 + -20 = -27.838821814 Simplifying x2 + -20 = -27.838821814 Reorder the terms: -20 + x2 = -27.838821814 Solving -20 + x2 = -27.838821814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x2 = -27.838821814 + 20 Combine like terms: -20 + 20 = 0 0 + x2 = -27.838821814 + 20 x2 = -27.838821814 + 20 Combine like terms: -27.838821814 + 20 = -7.838821814 x2 = -7.838821814 Simplifying x2 = -7.838821814 Reorder the terms: 7.838821814 + x2 = -7.838821814 + 7.838821814 Combine like terms: -7.838821814 + 7.838821814 = 0.000000000 7.838821814 + 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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