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Simplifying a(a + -3) = 120 Reorder the terms: a(-3 + a) = 120 (-3 * a + a * a) = 120 (-3a + a2) = 120 Solving -3a + a2 = 120 Solving for variable 'a'. Reorder the terms: -120 + -3a + a2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + -3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + -3a + 120 + a2 = 0 + 120 Reorder the terms: -120 + 120 + -3a + a2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -3a + a2 = 0 + 120 -3a + a2 = 0 + 120 Combine like terms: 0 + 120 = 120 -3a + a2 = 120 The a term is -3a. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3a + 2.25 + a2 = 120 + 2.25 Reorder the terms: 2.25 + -3a + a2 = 120 + 2.25 Combine like terms: 120 + 2.25 = 122.25 2.25 + -3a + a2 = 122.25 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (a + -1.5) equal to 11.056672194 and -11.056672194.Subproblem 1
a + -1.5 = 11.056672194 Simplifying a + -1.5 = 11.056672194 Reorder the terms: -1.5 + a = 11.056672194 Solving -1.5 + a = 11.056672194 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 11.056672194 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 11.056672194 + 1.5 a = 11.056672194 + 1.5 Combine like terms: 11.056672194 + 1.5 = 12.556672194 a = 12.556672194 Simplifying a = 12.556672194Subproblem 2
a + -1.5 = -11.056672194 Simplifying a + -1.5 = -11.056672194 Reorder the terms: -1.5 + a = -11.056672194 Solving -1.5 + a = -11.056672194 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -11.056672194 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -11.056672194 + 1.5 a = -11.056672194 + 1.5 Combine like terms: -11.056672194 + 1.5 = -9.556672194 a = -9.556672194 Simplifying a = -9.556672194Solution
The solution to the problem is based on the solutions from the subproblems. a = {12.556672194, -9.556672194}
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