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Simplifying -6(5r + 5) + 4r(4 + -5r) = 1 Reorder the terms: -6(5 + 5r) + 4r(4 + -5r) = 1 (5 * -6 + 5r * -6) + 4r(4 + -5r) = 1 (-30 + -30r) + 4r(4 + -5r) = 1 -30 + -30r + (4 * 4r + -5r * 4r) = 1 -30 + -30r + (16r + -20r2) = 1 Combine like terms: -30r + 16r = -14r -30 + -14r + -20r2 = 1 Solving -30 + -14r + -20r2 = 1 Solving for variable 'r'. Reorder the terms: -30 + -1 + -14r + -20r2 = 1 + -1 Combine like terms: -30 + -1 = -31 -31 + -14r + -20r2 = 1 + -1 Combine like terms: 1 + -1 = 0 -31 + -14r + -20r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(31 + 14r + 20r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(31 + 14r + 20r2)' equal to zero and attempt to solve: Simplifying 31 + 14r + 20r2 = 0 Solving 31 + 14r + 20r2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1.55 + 0.7r + r2 = 0.0 Move the constant term to the right: Add '-1.55' to each side of the equation. 1.55 + 0.7r + -1.55 + r2 = 0.0 + -1.55 Reorder the terms: 1.55 + -1.55 + 0.7r + r2 = 0.0 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + 0.7r + r2 = 0.0 + -1.55 0.7r + r2 = 0.0 + -1.55 Combine like terms: 0.0 + -1.55 = -1.55 0.7r + r2 = -1.55 The r term is 0.7r. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7r + 0.1225 + r2 = -1.55 + 0.1225 Reorder the terms: 0.1225 + 0.7r + r2 = -1.55 + 0.1225 Combine like terms: -1.55 + 0.1225 = -1.4275 0.1225 + 0.7r + r2 = -1.4275 Factor a perfect square on the left side: (r + 0.35)(r + 0.35) = -1.4275 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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