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Simplifying 5r2 + -10r + 23 = 8 Reorder the terms: 23 + -10r + 5r2 = 8 Solving 23 + -10r + 5r2 = 8 Solving for variable 'r'. Reorder the terms: 23 + -8 + -10r + 5r2 = 8 + -8 Combine like terms: 23 + -8 = 15 15 + -10r + 5r2 = 8 + -8 Combine like terms: 8 + -8 = 0 15 + -10r + 5r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -2r + r2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -2r + r2)' equal to zero and attempt to solve: Simplifying 3 + -2r + r2 = 0 Solving 3 + -2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2r + -3 + r2 = 0 + -3 Reorder the terms: 3 + -3 + -2r + r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2r + r2 = 0 + -3 -2r + r2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2r + r2 = -3 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 = -3 + 1 Reorder the terms: 1 + -2r + r2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + -2r + r2 = -2 Factor a perfect square on the left side: (r + -1)(r + -1) = -2 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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