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Simplifying 7x2 + 3ax = 10a2 Reorder the terms: 3ax + 7x2 = 10a2 Solving 3ax + 7x2 = 10a2 Solving for variable 'a'. Reorder the terms: 3ax + -10a2 + 7x2 = 10a2 + -10a2 Combine like terms: 10a2 + -10a2 = 0 3ax + -10a2 + 7x2 = 0 Factor a trinomial. (-10a + -7x)(a + -1x) = 0Subproblem 1
Set the factor '(-10a + -7x)' equal to zero and attempt to solve: Simplifying -10a + -7x = 0 Solving -10a + -7x = 0 Move all terms containing a to the left, all other terms to the right. Add '7x' to each side of the equation. -10a + -7x + 7x = 0 + 7x Combine like terms: -7x + 7x = 0 -10a + 0 = 0 + 7x -10a = 0 + 7x Remove the zero: -10a = 7x Divide each side by '-10'. a = -0.7x Simplifying a = -0.7xSubproblem 2
Set the factor '(a + -1x)' equal to zero and attempt to solve: Simplifying a + -1x = 0 Solving a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. a + -1x + x = 0 + x Combine like terms: -1x + x = 0 a + 0 = 0 + x a = 0 + x Remove the zero: a = x Simplifying a = xSolution
a = {-0.7x, x}
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