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Simplifying 45 + -14r + -1r2 = 0 Solving 45 + -14r + -1r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + 14r + r2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 14r + 45 + r2 = 0 + 45 Reorder the terms: -45 + 45 + 14r + r2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 14r + r2 = 0 + 45 14r + r2 = 0 + 45 Combine like terms: 0 + 45 = 45 14r + r2 = 45 The r term is 14r. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14r + 49 + r2 = 45 + 49 Reorder the terms: 49 + 14r + r2 = 45 + 49 Combine like terms: 45 + 49 = 94 49 + 14r + r2 = 94 Factor a perfect square on the left side: (r + 7)(r + 7) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (r + 7) equal to 9.695359715 and -9.695359715.Subproblem 1
r + 7 = 9.695359715 Simplifying r + 7 = 9.695359715 Reorder the terms: 7 + r = 9.695359715 Solving 7 + r = 9.695359715 Solving for variable 'r'. 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 = 9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + r = 9.695359715 + -7 r = 9.695359715 + -7 Combine like terms: 9.695359715 + -7 = 2.695359715 r = 2.695359715 Simplifying r = 2.695359715Subproblem 2
r + 7 = -9.695359715 Simplifying r + 7 = -9.695359715 Reorder the terms: 7 + r = -9.695359715 Solving 7 + r = -9.695359715 Solving for variable 'r'. 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 = -9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + r = -9.695359715 + -7 r = -9.695359715 + -7 Combine like terms: -9.695359715 + -7 = -16.695359715 r = -16.695359715 Simplifying r = -16.695359715Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.695359715, -16.695359715}
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