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Simplifying 4a2 + -28a + -143 = 0 Reorder the terms: -143 + -28a + 4a2 = 0 Solving -143 + -28a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -35.75 + -7a + a2 = 0 Move the constant term to the right: Add '35.75' to each side of the equation. -35.75 + -7a + 35.75 + a2 = 0 + 35.75 Reorder the terms: -35.75 + 35.75 + -7a + a2 = 0 + 35.75 Combine like terms: -35.75 + 35.75 = 0.00 0.00 + -7a + a2 = 0 + 35.75 -7a + a2 = 0 + 35.75 Combine like terms: 0 + 35.75 = 35.75 -7a + a2 = 35.75 The a term is -7a. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7a + 12.25 + a2 = 35.75 + 12.25 Reorder the terms: 12.25 + -7a + a2 = 35.75 + 12.25 Combine like terms: 35.75 + 12.25 = 48 12.25 + -7a + a2 = 48 Factor a perfect square on the left side: (a + -3.5)(a + -3.5) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (a + -3.5) equal to 6.92820323 and -6.92820323.Subproblem 1
a + -3.5 = 6.92820323 Simplifying a + -3.5 = 6.92820323 Reorder the terms: -3.5 + a = 6.92820323 Solving -3.5 + a = 6.92820323 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = 6.92820323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 6.92820323 + 3.5 a = 6.92820323 + 3.5 Combine like terms: 6.92820323 + 3.5 = 10.42820323 a = 10.42820323 Simplifying a = 10.42820323Subproblem 2
a + -3.5 = -6.92820323 Simplifying a + -3.5 = -6.92820323 Reorder the terms: -3.5 + a = -6.92820323 Solving -3.5 + a = -6.92820323 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = -6.92820323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -6.92820323 + 3.5 a = -6.92820323 + 3.5 Combine like terms: -6.92820323 + 3.5 = -3.42820323 a = -3.42820323 Simplifying a = -3.42820323Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.42820323, -3.42820323}
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