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Simplifying 7r2 = 70r + 175 Reorder the terms: 7r2 = 175 + 70r Solving 7r2 = 175 + 70r Solving for variable 'r'. Reorder the terms: -175 + -70r + 7r2 = 175 + 70r + -175 + -70r Reorder the terms: -175 + -70r + 7r2 = 175 + -175 + 70r + -70r Combine like terms: 175 + -175 = 0 -175 + -70r + 7r2 = 0 + 70r + -70r -175 + -70r + 7r2 = 70r + -70r Combine like terms: 70r + -70r = 0 -175 + -70r + 7r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-25 + -10r + r2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-25 + -10r + r2)' equal to zero and attempt to solve: Simplifying -25 + -10r + r2 = 0 Solving -25 + -10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -10r + 25 + r2 = 0 + 25 Reorder the terms: -25 + 25 + -10r + r2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -10r + r2 = 0 + 25 -10r + r2 = 0 + 25 Combine like terms: 0 + 25 = 25 -10r + r2 = 25 The r term is -10r. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10r + 25 + r2 = 25 + 25 Reorder the terms: 25 + -10r + r2 = 25 + 25 Combine like terms: 25 + 25 = 50 25 + -10r + r2 = 50 Factor a perfect square on the left side: (r + -5)(r + -5) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (r + -5) equal to 7.071067812 and -7.071067812.Subproblem 1
r + -5 = 7.071067812 Simplifying r + -5 = 7.071067812 Reorder the terms: -5 + r = 7.071067812 Solving -5 + r = 7.071067812 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + r = 7.071067812 + 5 r = 7.071067812 + 5 Combine like terms: 7.071067812 + 5 = 12.071067812 r = 12.071067812 Simplifying r = 12.071067812Subproblem 2
r + -5 = -7.071067812 Simplifying r + -5 = -7.071067812 Reorder the terms: -5 + r = -7.071067812 Solving -5 + r = -7.071067812 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + r = -7.071067812 + 5 r = -7.071067812 + 5 Combine like terms: -7.071067812 + 5 = -2.071067812 r = -2.071067812 Simplifying r = -2.071067812Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.071067812, -2.071067812}Solution
r = {12.071067812, -2.071067812}
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