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Simplifying 4a2 = 5a + 18 Reorder the terms: 4a2 = 18 + 5a Solving 4a2 = 18 + 5a Solving for variable 'a'. Reorder the terms: -18 + -5a + 4a2 = 18 + 5a + -18 + -5a Reorder the terms: -18 + -5a + 4a2 = 18 + -18 + 5a + -5a Combine like terms: 18 + -18 = 0 -18 + -5a + 4a2 = 0 + 5a + -5a -18 + -5a + 4a2 = 5a + -5a Combine like terms: 5a + -5a = 0 -18 + -5a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + -1.25a + a2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -1.25a + 4.5 + a2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -1.25a + a2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -1.25a + a2 = 0 + 4.5 -1.25a + a2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -1.25a + a2 = 4.5 The a term is -1.25a. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25a + 0.390625 + a2 = 4.5 + 0.390625 Reorder the terms: 0.390625 + -1.25a + a2 = 4.5 + 0.390625 Combine like terms: 4.5 + 0.390625 = 4.890625 0.390625 + -1.25a + a2 = 4.890625 Factor a perfect square on the left side: (a + -0.625)(a + -0.625) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (a + -0.625) equal to 2.211475752 and -2.211475752.Subproblem 1
a + -0.625 = 2.211475752 Simplifying a + -0.625 = 2.211475752 Reorder the terms: -0.625 + a = 2.211475752 Solving -0.625 + a = 2.211475752 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + a = 2.211475752 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + a = 2.211475752 + 0.625 a = 2.211475752 + 0.625 Combine like terms: 2.211475752 + 0.625 = 2.836475752 a = 2.836475752 Simplifying a = 2.836475752Subproblem 2
a + -0.625 = -2.211475752 Simplifying a + -0.625 = -2.211475752 Reorder the terms: -0.625 + a = -2.211475752 Solving -0.625 + a = -2.211475752 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + a = -2.211475752 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + a = -2.211475752 + 0.625 a = -2.211475752 + 0.625 Combine like terms: -2.211475752 + 0.625 = -1.586475752 a = -1.586475752 Simplifying a = -1.586475752Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.836475752, -1.586475752}
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