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Simplifying 7r + 2 = 5r(r + -4) Reorder the terms: 2 + 7r = 5r(r + -4) Reorder the terms: 2 + 7r = 5r(-4 + r) 2 + 7r = (-4 * 5r + r * 5r) 2 + 7r = (-20r + 5r2) Solving 2 + 7r = -20r + 5r2 Solving for variable 'r'. Combine like terms: 7r + 20r = 27r 2 + 27r + -5r2 = -20r + 5r2 + 20r + -5r2 Reorder the terms: 2 + 27r + -5r2 = -20r + 20r + 5r2 + -5r2 Combine like terms: -20r + 20r = 0 2 + 27r + -5r2 = 0 + 5r2 + -5r2 2 + 27r + -5r2 = 5r2 + -5r2 Combine like terms: 5r2 + -5r2 = 0 2 + 27r + -5r2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + -5.4r + r2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -5.4r + 0.4 + r2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -5.4r + r2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -5.4r + r2 = 0 + 0.4 -5.4r + r2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -5.4r + r2 = 0.4 The r term is -5.4r. Take half its coefficient (-2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. -5.4r + 7.29 + r2 = 0.4 + 7.29 Reorder the terms: 7.29 + -5.4r + r2 = 0.4 + 7.29 Combine like terms: 0.4 + 7.29 = 7.69 7.29 + -5.4r + r2 = 7.69 Factor a perfect square on the left side: (r + -2.7)(r + -2.7) = 7.69 Calculate the square root of the right side: 2.773084925 Break this problem into two subproblems by setting (r + -2.7) equal to 2.773084925 and -2.773084925.Subproblem 1
r + -2.7 = 2.773084925 Simplifying r + -2.7 = 2.773084925 Reorder the terms: -2.7 + r = 2.773084925 Solving -2.7 + r = 2.773084925 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + r = 2.773084925 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + r = 2.773084925 + 2.7 r = 2.773084925 + 2.7 Combine like terms: 2.773084925 + 2.7 = 5.473084925 r = 5.473084925 Simplifying r = 5.473084925Subproblem 2
r + -2.7 = -2.773084925 Simplifying r + -2.7 = -2.773084925 Reorder the terms: -2.7 + r = -2.773084925 Solving -2.7 + r = -2.773084925 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + r = -2.773084925 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + r = -2.773084925 + 2.7 r = -2.773084925 + 2.7 Combine like terms: -2.773084925 + 2.7 = -0.073084925 r = -0.073084925 Simplifying r = -0.073084925Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.473084925, -0.073084925}
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