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Simplifying 10x2 + -31ax + -14a2 = 0 Reorder the terms: -31ax + -14a2 + 10x2 = 0 Solving -31ax + -14a2 + 10x2 = 0 Solving for variable 'a'. Factor a trinomial. (-2a + -5x)(7a + -2x) = 0Subproblem 1
Set the factor '(-2a + -5x)' equal to zero and attempt to solve: Simplifying -2a + -5x = 0 Solving -2a + -5x = 0 Move all terms containing a to the left, all other terms to the right. Add '5x' to each side of the equation. -2a + -5x + 5x = 0 + 5x Combine like terms: -5x + 5x = 0 -2a + 0 = 0 + 5x -2a = 0 + 5x Remove the zero: -2a = 5x Divide each side by '-2'. a = -2.5x Simplifying a = -2.5xSubproblem 2
Set the factor '(7a + -2x)' equal to zero and attempt to solve: Simplifying 7a + -2x = 0 Solving 7a + -2x = 0 Move all terms containing a to the left, all other terms to the right. Add '2x' to each side of the equation. 7a + -2x + 2x = 0 + 2x Combine like terms: -2x + 2x = 0 7a + 0 = 0 + 2x 7a = 0 + 2x Remove the zero: 7a = 2x Divide each side by '7'. a = 0.2857142857x Simplifying a = 0.2857142857xSolution
a = {-2.5x, 0.2857142857x}
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