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Simplifying 10a2 + -19a + -35 = 0 Reorder the terms: -35 + -19a + 10a2 = 0 Solving -35 + -19a + 10a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3.5 + -1.9a + a2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -1.9a + 3.5 + a2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -1.9a + a2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -1.9a + a2 = 0 + 3.5 -1.9a + a2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -1.9a + a2 = 3.5 The a term is -1.9a. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9a + 0.9025 + a2 = 3.5 + 0.9025 Reorder the terms: 0.9025 + -1.9a + a2 = 3.5 + 0.9025 Combine like terms: 3.5 + 0.9025 = 4.4025 0.9025 + -1.9a + a2 = 4.4025 Factor a perfect square on the left side: (a + -0.95)(a + -0.95) = 4.4025 Calculate the square root of the right side: 2.098213526 Break this problem into two subproblems by setting (a + -0.95) equal to 2.098213526 and -2.098213526.Subproblem 1
a + -0.95 = 2.098213526 Simplifying a + -0.95 = 2.098213526 Reorder the terms: -0.95 + a = 2.098213526 Solving -0.95 + a = 2.098213526 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + a = 2.098213526 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + a = 2.098213526 + 0.95 a = 2.098213526 + 0.95 Combine like terms: 2.098213526 + 0.95 = 3.048213526 a = 3.048213526 Simplifying a = 3.048213526Subproblem 2
a + -0.95 = -2.098213526 Simplifying a + -0.95 = -2.098213526 Reorder the terms: -0.95 + a = -2.098213526 Solving -0.95 + a = -2.098213526 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + a = -2.098213526 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + a = -2.098213526 + 0.95 a = -2.098213526 + 0.95 Combine like terms: -2.098213526 + 0.95 = -1.148213526 a = -1.148213526 Simplifying a = -1.148213526Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.048213526, -1.148213526}
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