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Simplifying 6r6 + -6r3 = 84 Reorder the terms: -6r3 + 6r6 = 84 Solving -6r3 + 6r6 = 84 Solving for variable 'r'. Reorder the terms: -84 + -6r3 + 6r6 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + -6r3 + 6r6 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-14 + -1r3 + r6) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-14 + -1r3 + r6)' equal to zero and attempt to solve: Simplifying -14 + -1r3 + r6 = 0 Solving -14 + -1r3 + r6 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -1r3 + 14 + r6 = 0 + 14 Reorder the terms: -14 + 14 + -1r3 + r6 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1r3 + r6 = 0 + 14 -1r3 + r6 = 0 + 14 Combine like terms: 0 + 14 = 14 -1r3 + r6 = 14 The r term is -1r3. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1r3 + 0.25 + r6 = 14 + 0.25 Reorder the terms: 0.25 + -1r3 + r6 = 14 + 0.25 Combine like terms: 14 + 0.25 = 14.25 0.25 + -1r3 + r6 = 14.25 Factor a perfect square on the left side: (r3 + -0.5)(r3 + -0.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (r3 + -0.5) equal to 3.774917218 and -3.774917218.Subproblem 1
r3 + -0.5 = 3.774917218 Simplifying r3 + -0.5 = 3.774917218 Reorder the terms: -0.5 + r3 = 3.774917218 Solving -0.5 + r3 = 3.774917218 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r3 = 3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r3 = 3.774917218 + 0.5 r3 = 3.774917218 + 0.5 Combine like terms: 3.774917218 + 0.5 = 4.274917218 r3 = 4.274917218 Simplifying r3 = 4.274917218 Reorder the terms: -4.274917218 + r3 = 4.274917218 + -4.274917218 Combine like terms: 4.274917218 + -4.274917218 = 0.000000000 -4.274917218 + r3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
r3 + -0.5 = -3.774917218 Simplifying r3 + -0.5 = -3.774917218 Reorder the terms: -0.5 + r3 = -3.774917218 Solving -0.5 + r3 = -3.774917218 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r3 = -3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r3 = -3.774917218 + 0.5 r3 = -3.774917218 + 0.5 Combine like terms: -3.774917218 + 0.5 = -3.274917218 r3 = -3.274917218 Simplifying r3 = -3.274917218 Reorder the terms: 3.274917218 + r3 = -3.274917218 + 3.274917218 Combine like terms: -3.274917218 + 3.274917218 = 0.000000000 3.274917218 + r3 = 0.000000000 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. 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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