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Simplifying -4r2 + -7r + -4 = 6r2 Reorder the terms: -4 + -7r + -4r2 = 6r2 Solving -4 + -7r + -4r2 = 6r2 Solving for variable 'r'. Combine like terms: -4r2 + -6r2 = -10r2 -4 + -7r + -10r2 = 6r2 + -6r2 Combine like terms: 6r2 + -6r2 = 0 -4 + -7r + -10r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 7r + 10r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 7r + 10r2)' equal to zero and attempt to solve: Simplifying 4 + 7r + 10r2 = 0 Solving 4 + 7r + 10r2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.4 + 0.7r + r2 = 0.0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 0.7r + -0.4 + r2 = 0.0 + -0.4 Reorder the terms: 0.4 + -0.4 + 0.7r + r2 = 0.0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 0.7r + r2 = 0.0 + -0.4 0.7r + r2 = 0.0 + -0.4 Combine like terms: 0.0 + -0.4 = -0.4 0.7r + r2 = -0.4 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 = -0.4 + 0.1225 Reorder the terms: 0.1225 + 0.7r + r2 = -0.4 + 0.1225 Combine like terms: -0.4 + 0.1225 = -0.2775 0.1225 + 0.7r + r2 = -0.2775 Factor a perfect square on the left side: (r + 0.35)(r + 0.35) = -0.2775 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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