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Simplifying 6r4(4r2 + 5r + -2) = 0 Reorder the terms: 6r4(-2 + 5r + 4r2) = 0 (-2 * 6r4 + 5r * 6r4 + 4r2 * 6r4) = 0 (-12r4 + 30r5 + 24r6) = 0 Solving -12r4 + 30r5 + 24r6 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '6r4'. 6r4(-2 + 5r + 4r2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'r4' equal to zero and attempt to solve: Simplifying r4 = 0 Solving r4 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-2 + 5r + 4r2)' equal to zero and attempt to solve: Simplifying -2 + 5r + 4r2 = 0 Solving -2 + 5r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + 1.25r + r2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.25r + 0.5 + r2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.25r + r2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.25r + r2 = 0 + 0.5 1.25r + r2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.25r + r2 = 0.5 The r term is 1.25r. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25r + 0.390625 + r2 = 0.5 + 0.390625 Reorder the terms: 0.390625 + 1.25r + r2 = 0.5 + 0.390625 Combine like terms: 0.5 + 0.390625 = 0.890625 0.390625 + 1.25r + r2 = 0.890625 Factor a perfect square on the left side: (r + 0.625)(r + 0.625) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (r + 0.625) equal to 0.943729304 and -0.943729304.Subproblem 1
r + 0.625 = 0.943729304 Simplifying r + 0.625 = 0.943729304 Reorder the terms: 0.625 + r = 0.943729304 Solving 0.625 + r = 0.943729304 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + r = 0.943729304 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + r = 0.943729304 + -0.625 r = 0.943729304 + -0.625 Combine like terms: 0.943729304 + -0.625 = 0.318729304 r = 0.318729304 Simplifying r = 0.318729304Subproblem 2
r + 0.625 = -0.943729304 Simplifying r + 0.625 = -0.943729304 Reorder the terms: 0.625 + r = -0.943729304 Solving 0.625 + r = -0.943729304 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + r = -0.943729304 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + r = -0.943729304 + -0.625 r = -0.943729304 + -0.625 Combine like terms: -0.943729304 + -0.625 = -1.568729304 r = -1.568729304 Simplifying r = -1.568729304Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.318729304, -1.568729304}Solution
r = {0.318729304, -1.568729304}
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