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Simplifying r + -4(3r + 2) * r = 7 Reorder the terms: r + -4(2 + 3r) * r = 7 Reorder the terms for easier multiplication: r + -4r(2 + 3r) = 7 r + (2 * -4r + 3r * -4r) = 7 r + (-8r + -12r2) = 7 Combine like terms: r + -8r = -7r -7r + -12r2 = 7 Solving -7r + -12r2 = 7 Solving for variable 'r'. Reorder the terms: -7 + -7r + -12r2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -7r + -12r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 7r + 12r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 7r + 12r2)' equal to zero and attempt to solve: Simplifying 7 + 7r + 12r2 = 0 Solving 7 + 7r + 12r2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5833333333 + 0.5833333333r + r2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + 0.5833333333r + -0.5833333333 + r2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + 0.5833333333r + r2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + 0.5833333333r + r2 = 0 + -0.5833333333 0.5833333333r + r2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 0.5833333333r + r2 = -0.5833333333 The r term is 0.5833333333r. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333r + 0.08506944446 + r2 = -0.5833333333 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333r + r2 = -0.5833333333 + 0.08506944446 Combine like terms: -0.5833333333 + 0.08506944446 = -0.49826388884 0.08506944446 + 0.5833333333r + r2 = -0.49826388884 Factor a perfect square on the left side: (r + 0.2916666667)(r + 0.2916666667) = -0.49826388884 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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