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Simplifying (6r2) + 3r + -4 = 0 Reorder the terms: -4 + 3r + (6r2) = 0 Solving -4 + 3r + (6r2) = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.6666666667 + 0.5r + r2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.5r + 0.6666666667 + r2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.5r + r2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.5r + r2 = 0 + 0.6666666667 0.5r + r2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.5r + r2 = 0.6666666667 The r term is 0.5r. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5r + 0.0625 + r2 = 0.6666666667 + 0.0625 Reorder the terms: 0.0625 + 0.5r + r2 = 0.6666666667 + 0.0625 Combine like terms: 0.6666666667 + 0.0625 = 0.7291666667 0.0625 + 0.5r + r2 = 0.7291666667 Factor a perfect square on the left side: ((r) + 0.25)((r) + 0.25) = 0.7291666667 Calculate the square root of the right side: 0.853912564 Break this problem into two subproblems by setting ((r) + 0.25) equal to 0.853912564 and -0.853912564.Subproblem 1
(r) + 0.25 = 0.853912564 Simplifying (r) + 0.25 = 0.853912564 r + 0.25 = 0.853912564 Reorder the terms: 0.25 + r = 0.853912564 Solving 0.25 + r = 0.853912564 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + r = 0.853912564 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + r = 0.853912564 + -0.25 r = 0.853912564 + -0.25 Combine like terms: 0.853912564 + -0.25 = 0.603912564 r = 0.603912564 Simplifying r = 0.603912564Subproblem 2
(r) + 0.25 = -0.853912564 Simplifying (r) + 0.25 = -0.853912564 r + 0.25 = -0.853912564 Reorder the terms: 0.25 + r = -0.853912564 Solving 0.25 + r = -0.853912564 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + r = -0.853912564 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + r = -0.853912564 + -0.25 r = -0.853912564 + -0.25 Combine like terms: -0.853912564 + -0.25 = -1.103912564 r = -1.103912564 Simplifying r = -1.103912564Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.603912564, -1.103912564}
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