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Simplifying 10x4 + -66x2 = 56 Reorder the terms: -66x2 + 10x4 = 56 Solving -66x2 + 10x4 = 56 Solving for variable 'x'. Reorder the terms: -56 + -66x2 + 10x4 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + -66x2 + 10x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + -33x2 + 5x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + -33x2 + 5x4)' equal to zero and attempt to solve: Simplifying -28 + -33x2 + 5x4 = 0 Solving -28 + -33x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + -6.6x2 + x4 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -6.6x2 + 5.6 + x4 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -6.6x2 + x4 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -6.6x2 + x4 = 0 + 5.6 -6.6x2 + x4 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -6.6x2 + x4 = 5.6 The x term is -6.6x2. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6x2 + 10.89 + x4 = 5.6 + 10.89 Reorder the terms: 10.89 + -6.6x2 + x4 = 5.6 + 10.89 Combine like terms: 5.6 + 10.89 = 16.49 10.89 + -6.6x2 + x4 = 16.49 Factor a perfect square on the left side: (x2 + -3.3)(x2 + -3.3) = 16.49 Calculate the square root of the right side: 4.060788101 Break this problem into two subproblems by setting (x2 + -3.3) equal to 4.060788101 and -4.060788101.Subproblem 1
x2 + -3.3 = 4.060788101 Simplifying x2 + -3.3 = 4.060788101 Reorder the terms: -3.3 + x2 = 4.060788101 Solving -3.3 + x2 = 4.060788101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x2 = 4.060788101 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x2 = 4.060788101 + 3.3 x2 = 4.060788101 + 3.3 Combine like terms: 4.060788101 + 3.3 = 7.360788101 x2 = 7.360788101 Simplifying x2 = 7.360788101 Take the square root of each side: x = {-2.713077238, 2.713077238}Subproblem 2
x2 + -3.3 = -4.060788101 Simplifying x2 + -3.3 = -4.060788101 Reorder the terms: -3.3 + x2 = -4.060788101 Solving -3.3 + x2 = -4.060788101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x2 = -4.060788101 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x2 = -4.060788101 + 3.3 x2 = -4.060788101 + 3.3 Combine like terms: -4.060788101 + 3.3 = -0.760788101 x2 = -0.760788101 Simplifying x2 = -0.760788101 Reorder the terms: 0.760788101 + x2 = -0.760788101 + 0.760788101 Combine like terms: -0.760788101 + 0.760788101 = 0.000000000 0.760788101 + 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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