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Simplifying r2 + -8r + 10 = 0 Reorder the terms: 10 + -8r + r2 = 0 Solving 10 + -8r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8r + -10 + r2 = 0 + -10 Reorder the terms: 10 + -10 + -8r + r2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8r + r2 = 0 + -10 -8r + r2 = 0 + -10 Combine like terms: 0 + -10 = -10 -8r + r2 = -10 The r term is -8r. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8r + 16 + r2 = -10 + 16 Reorder the terms: 16 + -8r + r2 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + -8r + r2 = 6 Factor a perfect square on the left side: (r + -4)(r + -4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (r + -4) equal to 2.449489743 and -2.449489743.Subproblem 1
r + -4 = 2.449489743 Simplifying r + -4 = 2.449489743 Reorder the terms: -4 + r = 2.449489743 Solving -4 + r = 2.449489743 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + r = 2.449489743 + 4 r = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 r = 6.449489743 Simplifying r = 6.449489743Subproblem 2
r + -4 = -2.449489743 Simplifying r + -4 = -2.449489743 Reorder the terms: -4 + r = -2.449489743 Solving -4 + r = -2.449489743 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + r = -2.449489743 + 4 r = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 r = 1.550510257 Simplifying r = 1.550510257Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.449489743, 1.550510257}
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