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Simplifying 5r2 + -7 = 12r Reorder the terms: -7 + 5r2 = 12r Solving -7 + 5r2 = 12r Solving for variable 'r'. Reorder the terms: -7 + -12r + 5r2 = 12r + -12r Combine like terms: 12r + -12r = 0 -7 + -12r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -2.4r + r2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -2.4r + 1.4 + r2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -2.4r + r2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -2.4r + r2 = 0 + 1.4 -2.4r + r2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -2.4r + r2 = 1.4 The r term is -2.4r. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4r + 1.44 + r2 = 1.4 + 1.44 Reorder the terms: 1.44 + -2.4r + r2 = 1.4 + 1.44 Combine like terms: 1.4 + 1.44 = 2.84 1.44 + -2.4r + r2 = 2.84 Factor a perfect square on the left side: (r + -1.2)(r + -1.2) = 2.84 Calculate the square root of the right side: 1.685229955 Break this problem into two subproblems by setting (r + -1.2) equal to 1.685229955 and -1.685229955.Subproblem 1
r + -1.2 = 1.685229955 Simplifying r + -1.2 = 1.685229955 Reorder the terms: -1.2 + r = 1.685229955 Solving -1.2 + r = 1.685229955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + r = 1.685229955 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + r = 1.685229955 + 1.2 r = 1.685229955 + 1.2 Combine like terms: 1.685229955 + 1.2 = 2.885229955 r = 2.885229955 Simplifying r = 2.885229955Subproblem 2
r + -1.2 = -1.685229955 Simplifying r + -1.2 = -1.685229955 Reorder the terms: -1.2 + r = -1.685229955 Solving -1.2 + r = -1.685229955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + r = -1.685229955 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + r = -1.685229955 + 1.2 r = -1.685229955 + 1.2 Combine like terms: -1.685229955 + 1.2 = -0.485229955 r = -0.485229955 Simplifying r = -0.485229955Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.885229955, -0.485229955}
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