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Simplifying 42r2 = 56 + -1r Solving 42r2 = 56 + -1r Solving for variable 'r'. Reorder the terms: -56 + r + 42r2 = 56 + -1r + -56 + r Reorder the terms: -56 + r + 42r2 = 56 + -56 + -1r + r Combine like terms: 56 + -56 = 0 -56 + r + 42r2 = 0 + -1r + r -56 + r + 42r2 = -1r + r Combine like terms: -1r + r = 0 -56 + r + 42r2 = 0 Factor a trinomial. (-7 + -6r)(8 + -7r) = 0Subproblem 1
Set the factor '(-7 + -6r)' equal to zero and attempt to solve: Simplifying -7 + -6r = 0 Solving -7 + -6r = 0 Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -6r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6r = 0 + 7 -6r = 0 + 7 Combine like terms: 0 + 7 = 7 -6r = 7 Divide each side by '-6'. r = -1.166666667 Simplifying r = -1.166666667Subproblem 2
Set the factor '(8 + -7r)' equal to zero and attempt to solve: Simplifying 8 + -7r = 0 Solving 8 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7r = 0 + -8 -7r = 0 + -8 Combine like terms: 0 + -8 = -8 -7r = -8 Divide each side by '-7'. r = 1.142857143 Simplifying r = 1.142857143Solution
r = {-1.166666667, 1.142857143}
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