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Simplifying -2r2 + -56r + -22 = 0 Reorder the terms: -22 + -56r + -2r2 = 0 Solving -22 + -56r + -2r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '-2'. -2(11 + 28r + r2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(11 + 28r + r2)' equal to zero and attempt to solve: Simplifying 11 + 28r + r2 = 0 Solving 11 + 28r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 28r + -11 + r2 = 0 + -11 Reorder the terms: 11 + -11 + 28r + r2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 28r + r2 = 0 + -11 28r + r2 = 0 + -11 Combine like terms: 0 + -11 = -11 28r + r2 = -11 The r term is 28r. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28r + 196 + r2 = -11 + 196 Reorder the terms: 196 + 28r + r2 = -11 + 196 Combine like terms: -11 + 196 = 185 196 + 28r + r2 = 185 Factor a perfect square on the left side: (r + 14)(r + 14) = 185 Calculate the square root of the right side: 13.601470509 Break this problem into two subproblems by setting (r + 14) equal to 13.601470509 and -13.601470509.Subproblem 1
r + 14 = 13.601470509 Simplifying r + 14 = 13.601470509 Reorder the terms: 14 + r = 13.601470509 Solving 14 + r = 13.601470509 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + r = 13.601470509 + -14 Combine like terms: 14 + -14 = 0 0 + r = 13.601470509 + -14 r = 13.601470509 + -14 Combine like terms: 13.601470509 + -14 = -0.398529491 r = -0.398529491 Simplifying r = -0.398529491Subproblem 2
r + 14 = -13.601470509 Simplifying r + 14 = -13.601470509 Reorder the terms: 14 + r = -13.601470509 Solving 14 + r = -13.601470509 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + r = -13.601470509 + -14 Combine like terms: 14 + -14 = 0 0 + r = -13.601470509 + -14 r = -13.601470509 + -14 Combine like terms: -13.601470509 + -14 = -27.601470509 r = -27.601470509 Simplifying r = -27.601470509Solution
The solution to the problem is based on the solutions from the subproblems. r = {-0.398529491, -27.601470509}Solution
r = {-0.398529491, -27.601470509}
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