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Simplifying -3r2 + -5r = 7 Reorder the terms: -5r + -3r2 = 7 Solving -5r + -3r2 = 7 Solving for variable 'r'. Reorder the terms: -7 + -5r + -3r2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -5r + -3r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 5r + 3r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 5r + 3r2)' equal to zero and attempt to solve: Simplifying 7 + 5r + 3r2 = 0 Solving 7 + 5r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + 1.666666667r + r2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 1.666666667r + -2.333333333 + r2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 1.666666667r + r2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 1.666666667r + r2 = 0 + -2.333333333 1.666666667r + r2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 1.666666667r + r2 = -2.333333333 The r term is 1.666666667r. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667r + 0.6944444447 + r2 = -2.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667r + r2 = -2.333333333 + 0.6944444447 Combine like terms: -2.333333333 + 0.6944444447 = -1.6388888883 0.6944444447 + 1.666666667r + r2 = -1.6388888883 Factor a perfect square on the left side: (r + 0.8333333335)(r + 0.8333333335) = -1.6388888883 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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