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Simplifying 5r2 + -54r + -80 = 0 Reorder the terms: -80 + -54r + 5r2 = 0 Solving -80 + -54r + 5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16 + -10.8r + r2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -10.8r + 16 + r2 = 0 + 16 Reorder the terms: -16 + 16 + -10.8r + r2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -10.8r + r2 = 0 + 16 -10.8r + r2 = 0 + 16 Combine like terms: 0 + 16 = 16 -10.8r + r2 = 16 The r term is -10.8r. Take half its coefficient (-5.4). Square it (29.16) and add it to both sides. Add '29.16' to each side of the equation. -10.8r + 29.16 + r2 = 16 + 29.16 Reorder the terms: 29.16 + -10.8r + r2 = 16 + 29.16 Combine like terms: 16 + 29.16 = 45.16 29.16 + -10.8r + r2 = 45.16 Factor a perfect square on the left side: (r + -5.4)(r + -5.4) = 45.16 Calculate the square root of the right side: 6.720119047 Break this problem into two subproblems by setting (r + -5.4) equal to 6.720119047 and -6.720119047.Subproblem 1
r + -5.4 = 6.720119047 Simplifying r + -5.4 = 6.720119047 Reorder the terms: -5.4 + r = 6.720119047 Solving -5.4 + r = 6.720119047 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.4' to each side of the equation. -5.4 + 5.4 + r = 6.720119047 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + r = 6.720119047 + 5.4 r = 6.720119047 + 5.4 Combine like terms: 6.720119047 + 5.4 = 12.120119047 r = 12.120119047 Simplifying r = 12.120119047Subproblem 2
r + -5.4 = -6.720119047 Simplifying r + -5.4 = -6.720119047 Reorder the terms: -5.4 + r = -6.720119047 Solving -5.4 + r = -6.720119047 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.4' to each side of the equation. -5.4 + 5.4 + r = -6.720119047 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + r = -6.720119047 + 5.4 r = -6.720119047 + 5.4 Combine like terms: -6.720119047 + 5.4 = -1.320119047 r = -1.320119047 Simplifying r = -1.320119047Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.120119047, -1.320119047}
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