8r^2=6r-4

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Solution for 8r^2=6r-4 equation:


Simplifying
8r2 = 6r + -4

Reorder the terms:
8r2 = -4 + 6r

Solving
8r2 = -4 + 6r

Solving for variable 'r'.

Reorder the terms:
4 + -6r + 8r2 = -4 + 6r + 4 + -6r

Reorder the terms:
4 + -6r + 8r2 = -4 + 4 + 6r + -6r

Combine like terms: -4 + 4 = 0
4 + -6r + 8r2 = 0 + 6r + -6r
4 + -6r + 8r2 = 6r + -6r

Combine like terms: 6r + -6r = 0
4 + -6r + 8r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -3r + 4r2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + -3r + 4r2)' equal to zero and attempt to solve: Simplifying 2 + -3r + 4r2 = 0 Solving 2 + -3r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -0.75r + r2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.75r + -0.5 + r2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.75r + r2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.75r + r2 = 0 + -0.5 -0.75r + r2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.75r + r2 = -0.5 The r term is -0.75r. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75r + 0.140625 + r2 = -0.5 + 0.140625 Reorder the terms: 0.140625 + -0.75r + r2 = -0.5 + 0.140625 Combine like terms: -0.5 + 0.140625 = -0.359375 0.140625 + -0.75r + r2 = -0.359375 Factor a perfect square on the left side: (r + -0.375)(r + -0.375) = -0.359375 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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