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Simplifying 2a(3x + -7a) + -5x(2x + 4a) = 0 Reorder the terms: 2a(-7a + 3x) + -5x(2x + 4a) = 0 (-7a * 2a + 3x * 2a) + -5x(2x + 4a) = 0 Reorder the terms: (6ax + -14a2) + -5x(2x + 4a) = 0 (6ax + -14a2) + -5x(2x + 4a) = 0 Reorder the terms: 6ax + -14a2 + -5x(4a + 2x) = 0 6ax + -14a2 + (4a * -5x + 2x * -5x) = 0 6ax + -14a2 + (-20ax + -10x2) = 0 Reorder the terms: 6ax + -20ax + -14a2 + -10x2 = 0 Combine like terms: 6ax + -20ax = -14ax -14ax + -14a2 + -10x2 = 0 Solving -14ax + -14a2 + -10x2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-2'. -2(7ax + 7a2 + 5x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(7ax + 7a2 + 5x2)' equal to zero and attempt to solve: Simplifying 7ax + 7a2 + 5x2 = 0 Solving 7ax + 7a2 + 5x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. ax + a2 + 0.7142857143x2 = 0 Move the constant term to the right: Add '-0.7142857143x2' to each side of the equation. ax + a2 + 0.7142857143x2 + -0.7142857143x2 = 0 + -0.7142857143x2 Combine like terms: 0.7142857143x2 + -0.7142857143x2 = 0.0000000000 ax + a2 + 0.0000000000 = 0 + -0.7142857143x2 ax + a2 = 0 + -0.7142857143x2 Remove the zero: ax + a2 = -0.7142857143x2 The a term is ax. Take half its coefficient (0.5x). Square it (0.25x2) and add it to both sides. Add '0.25x2' to each side of the equation. x2 + a2 + 0.25x2 = -0.7142857143x2 + 0.25x2 Reorder the terms: a2 + x2 + 0.25x2 = -0.7142857143x2 + 0.25x2 Combine like terms: x2 + 0.25x2 = 1.25x2 a2 + 1.25x2 = -0.7142857143x2 + 0.25x2 Combine like terms: -0.7142857143x2 + 0.25x2 = -0.4642857143x2 a2 + 1.25x2 = -0.4642857143x2 Factor a perfect square on the left side: (a + 0.5x)(a + 0.5x) = -0.4642857143x2 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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