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Simplifying a2 + -10a + 13 = 7 Reorder the terms: 13 + -10a + a2 = 7 Solving 13 + -10a + a2 = 7 Solving for variable 'a'. Reorder the terms: 13 + -7 + -10a + a2 = 7 + -7 Combine like terms: 13 + -7 = 6 6 + -10a + a2 = 7 + -7 Combine like terms: 7 + -7 = 0 6 + -10a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -10a + -6 + a2 = 0 + -6 Reorder the terms: 6 + -6 + -10a + a2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -10a + a2 = 0 + -6 -10a + a2 = 0 + -6 Combine like terms: 0 + -6 = -6 -10a + a2 = -6 The a term is -10a. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10a + 25 + a2 = -6 + 25 Reorder the terms: 25 + -10a + a2 = -6 + 25 Combine like terms: -6 + 25 = 19 25 + -10a + a2 = 19 Factor a perfect square on the left side: (a + -5)(a + -5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (a + -5) equal to 4.358898944 and -4.358898944.Subproblem 1
a + -5 = 4.358898944 Simplifying a + -5 = 4.358898944 Reorder the terms: -5 + a = 4.358898944 Solving -5 + a = 4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + a = 4.358898944 + 5 a = 4.358898944 + 5 Combine like terms: 4.358898944 + 5 = 9.358898944 a = 9.358898944 Simplifying a = 9.358898944Subproblem 2
a + -5 = -4.358898944 Simplifying a + -5 = -4.358898944 Reorder the terms: -5 + a = -4.358898944 Solving -5 + a = -4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + a = -4.358898944 + 5 a = -4.358898944 + 5 Combine like terms: -4.358898944 + 5 = 0.641101056 a = 0.641101056 Simplifying a = 0.641101056Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.358898944, 0.641101056}
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