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Simplifying (13r + -2z)(13r + -2z) = 0 Multiply (13r + -2z) * (13r + -2z) (13r * (13r + -2z) + -2z * (13r + -2z)) = 0 ((13r * 13r + -2z * 13r) + -2z * (13r + -2z)) = 0 Reorder the terms: ((-26rz + 169r2) + -2z * (13r + -2z)) = 0 ((-26rz + 169r2) + -2z * (13r + -2z)) = 0 (-26rz + 169r2 + (13r * -2z + -2z * -2z)) = 0 (-26rz + 169r2 + (-26rz + 4z2)) = 0 Reorder the terms: (-26rz + -26rz + 169r2 + 4z2) = 0 Combine like terms: -26rz + -26rz = -52rz (-52rz + 169r2 + 4z2) = 0 Solving -52rz + 169r2 + 4z2 = 0 Solving for variable 'r'. Factor a trinomial. (13r + -2z)(13r + -2z) = 0Subproblem 1
Set the factor '(13r + -2z)' equal to zero and attempt to solve: Simplifying 13r + -2z = 0 Solving 13r + -2z = 0 Move all terms containing r to the left, all other terms to the right. Add '2z' to each side of the equation. 13r + -2z + 2z = 0 + 2z Combine like terms: -2z + 2z = 0 13r + 0 = 0 + 2z 13r = 0 + 2z Remove the zero: 13r = 2z Divide each side by '13'. r = 0.1538461538z Simplifying r = 0.1538461538zSubproblem 2
Set the factor '(13r + -2z)' equal to zero and attempt to solve: Simplifying 13r + -2z = 0 Solving 13r + -2z = 0 Move all terms containing r to the left, all other terms to the right. Add '2z' to each side of the equation. 13r + -2z + 2z = 0 + 2z Combine like terms: -2z + 2z = 0 13r + 0 = 0 + 2z 13r = 0 + 2z Remove the zero: 13r = 2z Divide each side by '13'. r = 0.1538461538z Simplifying r = 0.1538461538zSolution
r = {0.1538461538z, 0.1538461538z}
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