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Simplifying 965.3616 = 87.92r2 + 62.17r Reorder the terms: 965.3616 = 62.17r + 87.92r2 Solving 965.3616 = 62.17r + 87.92r2 Solving for variable 'r'. Reorder the terms: 965.3616 + -62.17r + -87.92r2 = 62.17r + -62.17r + 87.92r2 + -87.92r2 Combine like terms: 62.17r + -62.17r = 0.00 965.3616 + -62.17r + -87.92r2 = 0.00 + 87.92r2 + -87.92r2 965.3616 + -62.17r + -87.92r2 = 87.92r2 + -87.92r2 Combine like terms: 87.92r2 + -87.92r2 = 0.00 965.3616 + -62.17r + -87.92r2 = 0.00 Begin completing the square. Divide all terms by -87.92 the coefficient of the squared term: Divide each side by '-87.92'. -10.98 + 0.7071201092r + r2 = 0 Move the constant term to the right: Add '10.98' to each side of the equation. -10.98 + 0.7071201092r + 10.98 + r2 = 0 + 10.98 Reorder the terms: -10.98 + 10.98 + 0.7071201092r + r2 = 0 + 10.98 Combine like terms: -10.98 + 10.98 = 0.00 0.00 + 0.7071201092r + r2 = 0 + 10.98 0.7071201092r + r2 = 0 + 10.98 Combine like terms: 0 + 10.98 = 10.98 0.7071201092r + r2 = 10.98 The r term is 0.7071201092r. Take half its coefficient (0.3535600546). Square it (0.1250047122) and add it to both sides. Add '0.1250047122' to each side of the equation. 0.7071201092r + 0.1250047122 + r2 = 10.98 + 0.1250047122 Reorder the terms: 0.1250047122 + 0.7071201092r + r2 = 10.98 + 0.1250047122 Combine like terms: 10.98 + 0.1250047122 = 11.1050047122 0.1250047122 + 0.7071201092r + r2 = 11.1050047122 Factor a perfect square on the left side: (r + 0.3535600546)(r + 0.3535600546) = 11.1050047122 Calculate the square root of the right side: 3.332417248 Break this problem into two subproblems by setting (r + 0.3535600546) equal to 3.332417248 and -3.332417248.Subproblem 1
r + 0.3535600546 = 3.332417248 Simplifying r + 0.3535600546 = 3.332417248 Reorder the terms: 0.3535600546 + r = 3.332417248 Solving 0.3535600546 + r = 3.332417248 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.3535600546' to each side of the equation. 0.3535600546 + -0.3535600546 + r = 3.332417248 + -0.3535600546 Combine like terms: 0.3535600546 + -0.3535600546 = 0.0000000000 0.0000000000 + r = 3.332417248 + -0.3535600546 r = 3.332417248 + -0.3535600546 Combine like terms: 3.332417248 + -0.3535600546 = 2.9788571934 r = 2.9788571934 Simplifying r = 2.9788571934Subproblem 2
r + 0.3535600546 = -3.332417248 Simplifying r + 0.3535600546 = -3.332417248 Reorder the terms: 0.3535600546 + r = -3.332417248 Solving 0.3535600546 + r = -3.332417248 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.3535600546' to each side of the equation. 0.3535600546 + -0.3535600546 + r = -3.332417248 + -0.3535600546 Combine like terms: 0.3535600546 + -0.3535600546 = 0.0000000000 0.0000000000 + r = -3.332417248 + -0.3535600546 r = -3.332417248 + -0.3535600546 Combine like terms: -3.332417248 + -0.3535600546 = -3.6859773026 r = -3.6859773026 Simplifying r = -3.6859773026Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.9788571934, -3.6859773026}
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