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Simplifying 5a + 3 = 4a2 Reorder the terms: 3 + 5a = 4a2 Solving 3 + 5a = 4a2 Solving for variable 'a'. Combine like terms: 4a2 + -4a2 = 0 3 + 5a + -4a2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -1.25a + a2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.25a + 0.75 + a2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.25a + a2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.25a + a2 = 0 + 0.75 -1.25a + a2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.25a + a2 = 0.75 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 = 0.75 + 0.390625 Reorder the terms: 0.390625 + -1.25a + a2 = 0.75 + 0.390625 Combine like terms: 0.75 + 0.390625 = 1.140625 0.390625 + -1.25a + a2 = 1.140625 Factor a perfect square on the left side: (a + -0.625)(a + -0.625) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (a + -0.625) equal to 1.068000468 and -1.068000468.Subproblem 1
a + -0.625 = 1.068000468 Simplifying a + -0.625 = 1.068000468 Reorder the terms: -0.625 + a = 1.068000468 Solving -0.625 + a = 1.068000468 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 = 1.068000468 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + a = 1.068000468 + 0.625 a = 1.068000468 + 0.625 Combine like terms: 1.068000468 + 0.625 = 1.693000468 a = 1.693000468 Simplifying a = 1.693000468Subproblem 2
a + -0.625 = -1.068000468 Simplifying a + -0.625 = -1.068000468 Reorder the terms: -0.625 + a = -1.068000468 Solving -0.625 + a = -1.068000468 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 = -1.068000468 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + a = -1.068000468 + 0.625 a = -1.068000468 + 0.625 Combine like terms: -1.068000468 + 0.625 = -0.443000468 a = -0.443000468 Simplifying a = -0.443000468Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.693000468, -0.443000468}
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