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Simplifying 35r5 + -42r4 + 14r3 = 0 Reorder the terms: 14r3 + -42r4 + 35r5 = 0 Solving 14r3 + -42r4 + 35r5 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '7r3'. 7r3(2 + -6r + 5r2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'r3' equal to zero and attempt to solve: Simplifying r3 = 0 Solving r3 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r3 = 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 '(2 + -6r + 5r2)' equal to zero and attempt to solve: Simplifying 2 + -6r + 5r2 = 0 Solving 2 + -6r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -1.2r + r2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1.2r + -0.4 + r2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1.2r + r2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1.2r + r2 = 0 + -0.4 -1.2r + r2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1.2r + r2 = -0.4 The r term is -1.2r. 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. -1.2r + 0.36 + r2 = -0.4 + 0.36 Reorder the terms: 0.36 + -1.2r + r2 = -0.4 + 0.36 Combine like terms: -0.4 + 0.36 = -0.04 0.36 + -1.2r + r2 = -0.04 Factor a perfect square on the left side: (r + -0.6)(r + -0.6) = -0.04 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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