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Simplifying 42r3t + 35r2t + 28rt = 0 Reorder the terms: 28rt + 35r2t + 42r3t = 0 Solving 28rt + 35r2t + 42r3t = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '7rt'. 7rt(4 + 5r + 6r2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'rt' equal to zero and attempt to solve: Simplifying rt = 0 Solving rt = 0 Move all terms containing r to the left, all other terms to the right. Simplifying rt = 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 '(4 + 5r + 6r2)' equal to zero and attempt to solve: Simplifying 4 + 5r + 6r2 = 0 Solving 4 + 5r + 6r2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + 0.8333333333r + r2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 0.8333333333r + -0.6666666667 + r2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 0.8333333333r + r2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 0.8333333333r + r2 = 0 + -0.6666666667 0.8333333333r + r2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 0.8333333333r + r2 = -0.6666666667 The r term is 0.8333333333r. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333r + 0.1736111111 + r2 = -0.6666666667 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333r + r2 = -0.6666666667 + 0.1736111111 Combine like terms: -0.6666666667 + 0.1736111111 = -0.4930555556 0.1736111111 + 0.8333333333r + r2 = -0.4930555556 Factor a perfect square on the left side: (r + 0.4166666667)(r + 0.4166666667) = -0.4930555556 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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