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Simplifying 2(a + -20) + 2a = 5a(a + -3) + -2 Reorder the terms: 2(-20 + a) + 2a = 5a(a + -3) + -2 (-20 * 2 + a * 2) + 2a = 5a(a + -3) + -2 (-40 + 2a) + 2a = 5a(a + -3) + -2 Combine like terms: 2a + 2a = 4a -40 + 4a = 5a(a + -3) + -2 Reorder the terms: -40 + 4a = 5a(-3 + a) + -2 -40 + 4a = (-3 * 5a + a * 5a) + -2 -40 + 4a = (-15a + 5a2) + -2 Reorder the terms: -40 + 4a = -2 + -15a + 5a2 Solving -40 + 4a = -2 + -15a + 5a2 Solving for variable 'a'. Reorder the terms: -40 + 2 + 4a + 15a + -5a2 = -2 + -15a + 5a2 + 2 + 15a + -5a2 Combine like terms: -40 + 2 = -38 -38 + 4a + 15a + -5a2 = -2 + -15a + 5a2 + 2 + 15a + -5a2 Combine like terms: 4a + 15a = 19a -38 + 19a + -5a2 = -2 + -15a + 5a2 + 2 + 15a + -5a2 Reorder the terms: -38 + 19a + -5a2 = -2 + 2 + -15a + 15a + 5a2 + -5a2 Combine like terms: -2 + 2 = 0 -38 + 19a + -5a2 = 0 + -15a + 15a + 5a2 + -5a2 -38 + 19a + -5a2 = -15a + 15a + 5a2 + -5a2 Combine like terms: -15a + 15a = 0 -38 + 19a + -5a2 = 0 + 5a2 + -5a2 -38 + 19a + -5a2 = 5a2 + -5a2 Combine like terms: 5a2 + -5a2 = 0 -38 + 19a + -5a2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 7.6 + -3.8a + a2 = 0 Move the constant term to the right: Add '-7.6' to each side of the equation. 7.6 + -3.8a + -7.6 + a2 = 0 + -7.6 Reorder the terms: 7.6 + -7.6 + -3.8a + a2 = 0 + -7.6 Combine like terms: 7.6 + -7.6 = 0.0 0.0 + -3.8a + a2 = 0 + -7.6 -3.8a + a2 = 0 + -7.6 Combine like terms: 0 + -7.6 = -7.6 -3.8a + a2 = -7.6 The a term is -3.8a. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8a + 3.61 + a2 = -7.6 + 3.61 Reorder the terms: 3.61 + -3.8a + a2 = -7.6 + 3.61 Combine like terms: -7.6 + 3.61 = -3.99 3.61 + -3.8a + a2 = -3.99 Factor a perfect square on the left side: (a + -1.9)(a + -1.9) = -3.99 Can't calculate square root of the right side. The solution to this equation could not be determined.
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