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Simplifying 5r2 + 42r + 42 = -7 Reorder the terms: 42 + 42r + 5r2 = -7 Solving 42 + 42r + 5r2 = -7 Solving for variable 'r'. Reorder the terms: 42 + 7 + 42r + 5r2 = -7 + 7 Combine like terms: 42 + 7 = 49 49 + 42r + 5r2 = -7 + 7 Combine like terms: -7 + 7 = 0 49 + 42r + 5r2 = 0 Factor a trinomial. (7 + r)(7 + 5r) = 0Subproblem 1
Set the factor '(7 + r)' equal to zero and attempt to solve: Simplifying 7 + r = 0 Solving 7 + r = 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 + r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + r = 0 + -7 r = 0 + -7 Combine like terms: 0 + -7 = -7 r = -7 Simplifying r = -7Subproblem 2
Set the factor '(7 + 5r)' equal to zero and attempt to solve: Simplifying 7 + 5r = 0 Solving 7 + 5r = 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 + 5r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5r = 0 + -7 5r = 0 + -7 Combine like terms: 0 + -7 = -7 5r = -7 Divide each side by '5'. r = -1.4 Simplifying r = -1.4Solution
r = {-7, -1.4}
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