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Simplifying 10r2 + -10r + -12 = 0 Reorder the terms: -12 + -10r + 10r2 = 0 Solving -12 + -10r + 10r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -5r + 5r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -5r + 5r2)' equal to zero and attempt to solve: Simplifying -6 + -5r + 5r2 = 0 Solving -6 + -5r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -1r + r2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -1r + 1.2 + r2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -1r + r2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -1r + r2 = 0 + 1.2 -1r + r2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -1r + r2 = 1.2 The r term is -1r. 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 = 1.2 + 0.25 Reorder the terms: 0.25 + -1r + r2 = 1.2 + 0.25 Combine like terms: 1.2 + 0.25 = 1.45 0.25 + -1r + r2 = 1.45 Factor a perfect square on the left side: (r + -0.5)(r + -0.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (r + -0.5) equal to 1.204159458 and -1.204159458.Subproblem 1
r + -0.5 = 1.204159458 Simplifying r + -0.5 = 1.204159458 Reorder the terms: -0.5 + r = 1.204159458 Solving -0.5 + r = 1.204159458 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 = 1.204159458 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 1.204159458 + 0.5 r = 1.204159458 + 0.5 Combine like terms: 1.204159458 + 0.5 = 1.704159458 r = 1.704159458 Simplifying r = 1.704159458Subproblem 2
r + -0.5 = -1.204159458 Simplifying r + -0.5 = -1.204159458 Reorder the terms: -0.5 + r = -1.204159458 Solving -0.5 + r = -1.204159458 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 = -1.204159458 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -1.204159458 + 0.5 r = -1.204159458 + 0.5 Combine like terms: -1.204159458 + 0.5 = -0.704159458 r = -0.704159458 Simplifying r = -0.704159458Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.704159458, -0.704159458}Solution
r = {1.704159458, -0.704159458}
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