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Simplifying 42r2 + 12r + 54 = 0 Reorder the terms: 54 + 12r + 42r2 = 0 Solving 54 + 12r + 42r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '6'. 6(9 + 2r + 7r2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(9 + 2r + 7r2)' equal to zero and attempt to solve: Simplifying 9 + 2r + 7r2 = 0 Solving 9 + 2r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.285714286 + 0.2857142857r + r2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + 0.2857142857r + -1.285714286 + r2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + 0.2857142857r + r2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + 0.2857142857r + r2 = 0 + -1.285714286 0.2857142857r + r2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 0.2857142857r + r2 = -1.285714286 The r term is 0.2857142857r. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857r + 0.02040816328 + r2 = -1.285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857r + r2 = -1.285714286 + 0.02040816328 Combine like terms: -1.285714286 + 0.02040816328 = -1.26530612272 0.02040816328 + 0.2857142857r + r2 = -1.26530612272 Factor a perfect square on the left side: (r + 0.1428571429)(r + 0.1428571429) = -1.26530612272 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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