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Simplifying 10r2 + 20r + -49 = -7 Reorder the terms: -49 + 20r + 10r2 = -7 Solving -49 + 20r + 10r2 = -7 Solving for variable 'r'. Reorder the terms: -49 + 7 + 20r + 10r2 = -7 + 7 Combine like terms: -49 + 7 = -42 -42 + 20r + 10r2 = -7 + 7 Combine like terms: -7 + 7 = 0 -42 + 20r + 10r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 10r + 5r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + 10r + 5r2)' equal to zero and attempt to solve: Simplifying -21 + 10r + 5r2 = 0 Solving -21 + 10r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + 2r + r2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 2r + 4.2 + r2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 2r + r2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 2r + r2 = 0 + 4.2 2r + r2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 2r + r2 = 4.2 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 4.2 + 1 Reorder the terms: 1 + 2r + r2 = 4.2 + 1 Combine like terms: 4.2 + 1 = 5.2 1 + 2r + r2 = 5.2 Factor a perfect square on the left side: (r + 1)(r + 1) = 5.2 Calculate the square root of the right side: 2.28035085 Break this problem into two subproblems by setting (r + 1) equal to 2.28035085 and -2.28035085.Subproblem 1
r + 1 = 2.28035085 Simplifying r + 1 = 2.28035085 Reorder the terms: 1 + r = 2.28035085 Solving 1 + r = 2.28035085 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 2.28035085 + -1 Combine like terms: 1 + -1 = 0 0 + r = 2.28035085 + -1 r = 2.28035085 + -1 Combine like terms: 2.28035085 + -1 = 1.28035085 r = 1.28035085 Simplifying r = 1.28035085Subproblem 2
r + 1 = -2.28035085 Simplifying r + 1 = -2.28035085 Reorder the terms: 1 + r = -2.28035085 Solving 1 + r = -2.28035085 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -2.28035085 + -1 Combine like terms: 1 + -1 = 0 0 + r = -2.28035085 + -1 r = -2.28035085 + -1 Combine like terms: -2.28035085 + -1 = -3.28035085 r = -3.28035085 Simplifying r = -3.28035085Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.28035085, -3.28035085}Solution
r = {1.28035085, -3.28035085}
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