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Simplifying 20x7 + -24x6 + 72x5 = 0 Reorder the terms: 72x5 + -24x6 + 20x7 = 0 Solving 72x5 + -24x6 + 20x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x5'. 4x5(18 + -6x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x5' equal to zero and attempt to solve: Simplifying x5 = 0 Solving x5 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(18 + -6x + 5x2)' equal to zero and attempt to solve: Simplifying 18 + -6x + 5x2 = 0 Solving 18 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.6 + -1.2x + x2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -1.2x + -3.6 + x2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -1.2x + x2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -1.2x + x2 = 0 + -3.6 -1.2x + x2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -1.2x + x2 = -3.6 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -3.6 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -3.6 + 0.36 Combine like terms: -3.6 + 0.36 = -3.24 0.36 + -1.2x + x2 = -3.24 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = -3.24 Can't calculate square root of the right side. 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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