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Simplifying 8r * 8r + 16r + 14 = 8 Reorder the terms for easier multiplication: 8 * 8r * r + 16r + 14 = 8 Multiply 8 * 8 64r * r + 16r + 14 = 8 Multiply r * r 64r2 + 16r + 14 = 8 Reorder the terms: 14 + 16r + 64r2 = 8 Solving 14 + 16r + 64r2 = 8 Solving for variable 'r'. Reorder the terms: 14 + -8 + 16r + 64r2 = 8 + -8 Combine like terms: 14 + -8 = 6 6 + 16r + 64r2 = 8 + -8 Combine like terms: 8 + -8 = 0 6 + 16r + 64r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 8r + 32r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 8r + 32r2)' equal to zero and attempt to solve: Simplifying 3 + 8r + 32r2 = 0 Solving 3 + 8r + 32r2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.09375 + 0.25r + r2 = 0 Move the constant term to the right: Add '-0.09375' to each side of the equation. 0.09375 + 0.25r + -0.09375 + r2 = 0 + -0.09375 Reorder the terms: 0.09375 + -0.09375 + 0.25r + r2 = 0 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + 0.25r + r2 = 0 + -0.09375 0.25r + r2 = 0 + -0.09375 Combine like terms: 0 + -0.09375 = -0.09375 0.25r + r2 = -0.09375 The r term is 0.25r. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25r + 0.015625 + r2 = -0.09375 + 0.015625 Reorder the terms: 0.015625 + 0.25r + r2 = -0.09375 + 0.015625 Combine like terms: -0.09375 + 0.015625 = -0.078125 0.015625 + 0.25r + r2 = -0.078125 Factor a perfect square on the left side: (r + 0.125)(r + 0.125) = -0.078125 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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