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Simplifying -5r6 + 4r5 + -75r4 = 0 Reorder the terms: -75r4 + 4r5 + -5r6 = 0 Solving -75r4 + 4r5 + -5r6 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r4'. r4(-75 + 4r + -5r2) = 0Subproblem 1
Set the factor 'r4' equal to zero and attempt to solve: Simplifying r4 = 0 Solving r4 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r4 = 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 '(-75 + 4r + -5r2)' equal to zero and attempt to solve: Simplifying -75 + 4r + -5r2 = 0 Solving -75 + 4r + -5r2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 15 + -0.8r + r2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -0.8r + -15 + r2 = 0 + -15 Reorder the terms: 15 + -15 + -0.8r + r2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -0.8r + r2 = 0 + -15 -0.8r + r2 = 0 + -15 Combine like terms: 0 + -15 = -15 -0.8r + r2 = -15 The r term is -0.8r. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8r + 0.16 + r2 = -15 + 0.16 Reorder the terms: 0.16 + -0.8r + r2 = -15 + 0.16 Combine like terms: -15 + 0.16 = -14.84 0.16 + -0.8r + r2 = -14.84 Factor a perfect square on the left side: (r + -0.4)(r + -0.4) = -14.84 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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