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Simplifying 15x4 + 156x2 + 9 = 0 Reorder the terms: 9 + 156x2 + 15x4 = 0 Solving 9 + 156x2 + 15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 52x2 + 5x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 52x2 + 5x4)' equal to zero and attempt to solve: Simplifying 3 + 52x2 + 5x4 = 0 Solving 3 + 52x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 10.4x2 + x4 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 10.4x2 + -0.6 + x4 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 10.4x2 + x4 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 10.4x2 + x4 = 0 + -0.6 10.4x2 + x4 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 10.4x2 + x4 = -0.6 The x term is 10.4x2. Take half its coefficient (5.2). Square it (27.04) and add it to both sides. Add '27.04' to each side of the equation. 10.4x2 + 27.04 + x4 = -0.6 + 27.04 Reorder the terms: 27.04 + 10.4x2 + x4 = -0.6 + 27.04 Combine like terms: -0.6 + 27.04 = 26.44 27.04 + 10.4x2 + x4 = 26.44 Factor a perfect square on the left side: (x2 + 5.2)(x2 + 5.2) = 26.44 Calculate the square root of the right side: 5.141984053 Break this problem into two subproblems by setting (x2 + 5.2) equal to 5.141984053 and -5.141984053.Subproblem 1
x2 + 5.2 = 5.141984053 Simplifying x2 + 5.2 = 5.141984053 Reorder the terms: 5.2 + x2 = 5.141984053 Solving 5.2 + x2 = 5.141984053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.2' to each side of the equation. 5.2 + -5.2 + x2 = 5.141984053 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + x2 = 5.141984053 + -5.2 x2 = 5.141984053 + -5.2 Combine like terms: 5.141984053 + -5.2 = -0.058015947 x2 = -0.058015947 Simplifying x2 = -0.058015947 Reorder the terms: 0.058015947 + x2 = -0.058015947 + 0.058015947 Combine like terms: -0.058015947 + 0.058015947 = 0.000000000 0.058015947 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 5.2 = -5.141984053 Simplifying x2 + 5.2 = -5.141984053 Reorder the terms: 5.2 + x2 = -5.141984053 Solving 5.2 + x2 = -5.141984053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.2' to each side of the equation. 5.2 + -5.2 + x2 = -5.141984053 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + x2 = -5.141984053 + -5.2 x2 = -5.141984053 + -5.2 Combine like terms: -5.141984053 + -5.2 = -10.341984053 x2 = -10.341984053 Simplifying x2 = -10.341984053 Reorder the terms: 10.341984053 + x2 = -10.341984053 + 10.341984053 Combine like terms: -10.341984053 + 10.341984053 = 0.000000000 10.341984053 + 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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