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Simplifying 4a2 + -9 = a Reorder the terms: -9 + 4a2 = a Solving -9 + 4a2 = a Solving for variable 'a'. Reorder the terms: -9 + -1a + 4a2 = a + -1a Combine like terms: a + -1a = 0 -9 + -1a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -0.25a + a2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.25a + 2.25 + a2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.25a + a2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.25a + a2 = 0 + 2.25 -0.25a + a2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.25a + a2 = 2.25 The a term is -0.25a. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25a + 0.015625 + a2 = 2.25 + 0.015625 Reorder the terms: 0.015625 + -0.25a + a2 = 2.25 + 0.015625 Combine like terms: 2.25 + 0.015625 = 2.265625 0.015625 + -0.25a + a2 = 2.265625 Factor a perfect square on the left side: (a + -0.125)(a + -0.125) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (a + -0.125) equal to 1.505199322 and -1.505199322.Subproblem 1
a + -0.125 = 1.505199322 Simplifying a + -0.125 = 1.505199322 Reorder the terms: -0.125 + a = 1.505199322 Solving -0.125 + a = 1.505199322 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + a = 1.505199322 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + a = 1.505199322 + 0.125 a = 1.505199322 + 0.125 Combine like terms: 1.505199322 + 0.125 = 1.630199322 a = 1.630199322 Simplifying a = 1.630199322Subproblem 2
a + -0.125 = -1.505199322 Simplifying a + -0.125 = -1.505199322 Reorder the terms: -0.125 + a = -1.505199322 Solving -0.125 + a = -1.505199322 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + a = -1.505199322 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + a = -1.505199322 + 0.125 a = -1.505199322 + 0.125 Combine like terms: -1.505199322 + 0.125 = -1.380199322 a = -1.380199322 Simplifying a = -1.380199322Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.630199322, -1.380199322}
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