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Simplifying x(2x + 7a) = 60a2 Reorder the terms: x(7a + 2x) = 60a2 (7a * x + 2x * x) = 60a2 (7ax + 2x2) = 60a2 Solving 7ax + 2x2 = 60a2 Solving for variable 'a'. Reorder the terms: 7ax + -60a2 + 2x2 = 60a2 + -60a2 Combine like terms: 60a2 + -60a2 = 0 7ax + -60a2 + 2x2 = 0 Factor a trinomial. (-15a + -2x)(4a + -1x) = 0Subproblem 1
Set the factor '(-15a + -2x)' equal to zero and attempt to solve: Simplifying -15a + -2x = 0 Solving -15a + -2x = 0 Move all terms containing a to the left, all other terms to the right. Add '2x' to each side of the equation. -15a + -2x + 2x = 0 + 2x Combine like terms: -2x + 2x = 0 -15a + 0 = 0 + 2x -15a = 0 + 2x Remove the zero: -15a = 2x Divide each side by '-15'. a = -0.1333333333x Simplifying a = -0.1333333333xSubproblem 2
Set the factor '(4a + -1x)' equal to zero and attempt to solve: Simplifying 4a + -1x = 0 Solving 4a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. 4a + -1x + x = 0 + x Combine like terms: -1x + x = 0 4a + 0 = 0 + x 4a = 0 + x Remove the zero: 4a = x Divide each side by '4'. a = 0.25x Simplifying a = 0.25xSolution
a = {-0.1333333333x, 0.25x}
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