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Simplifying r + -3 + 25 = r2 Reorder the terms: -3 + 25 + r = r2 Combine like terms: -3 + 25 = 22 22 + r = r2 Solving 22 + r = r2 Solving for variable 'r'. Combine like terms: r2 + -1r2 = 0 22 + r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -22 + -1r + r2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + -1r + 22 + r2 = 0 + 22 Reorder the terms: -22 + 22 + -1r + r2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -1r + r2 = 0 + 22 -1r + r2 = 0 + 22 Combine like terms: 0 + 22 = 22 -1r + r2 = 22 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1r + 0.25 + r2 = 22 + 0.25 Reorder the terms: 0.25 + -1r + r2 = 22 + 0.25 Combine like terms: 22 + 0.25 = 22.25 0.25 + -1r + r2 = 22.25 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (r + 0.5) equal to 4.716990566 and -4.716990566.Subproblem 1
r + 0.5 = 4.716990566 Simplifying r + 0.5 = 4.716990566 Reorder the terms: 0.5 + r = 4.716990566 Solving 0.5 + r = 4.716990566 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 4.716990566 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 4.716990566 + -0.5 r = 4.716990566 + -0.5 Combine like terms: 4.716990566 + -0.5 = 4.216990566 r = 4.216990566 Simplifying r = 4.216990566Subproblem 2
r + 0.5 = -4.716990566 Simplifying r + 0.5 = -4.716990566 Reorder the terms: 0.5 + r = -4.716990566 Solving 0.5 + r = -4.716990566 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -4.716990566 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -4.716990566 + -0.5 r = -4.716990566 + -0.5 Combine like terms: -4.716990566 + -0.5 = -5.216990566 r = -5.216990566 Simplifying r = -5.216990566Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.216990566, -5.216990566}
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