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Simplifying 0 = 2r2 + -10r + 14 Reorder the terms: 0 = 14 + -10r + 2r2 Solving 0 = 14 + -10r + 2r2 Solving for variable 'r'. Combine like terms: 0 + -14 = -14 -14 + 10r + -2r2 = 14 + -10r + 2r2 + -14 + 10r + -2r2 Reorder the terms: -14 + 10r + -2r2 = 14 + -14 + -10r + 10r + 2r2 + -2r2 Combine like terms: 14 + -14 = 0 -14 + 10r + -2r2 = 0 + -10r + 10r + 2r2 + -2r2 -14 + 10r + -2r2 = -10r + 10r + 2r2 + -2r2 Combine like terms: -10r + 10r = 0 -14 + 10r + -2r2 = 0 + 2r2 + -2r2 -14 + 10r + -2r2 = 2r2 + -2r2 Combine like terms: 2r2 + -2r2 = 0 -14 + 10r + -2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 5r + -1r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 5r + -1r2)' equal to zero and attempt to solve: Simplifying -7 + 5r + -1r2 = 0 Solving -7 + 5r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -5r + r2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -5r + -7 + r2 = 0 + -7 Reorder the terms: 7 + -7 + -5r + r2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5r + r2 = 0 + -7 -5r + r2 = 0 + -7 Combine like terms: 0 + -7 = -7 -5r + r2 = -7 The r term is -5r. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5r + 6.25 + r2 = -7 + 6.25 Reorder the terms: 6.25 + -5r + r2 = -7 + 6.25 Combine like terms: -7 + 6.25 = -0.75 6.25 + -5r + r2 = -0.75 Factor a perfect square on the left side: (r + -2.5)(r + -2.5) = -0.75 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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