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Simplifying a(a2 + 2a + -10) = 0 Reorder the terms: a(-10 + 2a + a2) = 0 (-10 * a + 2a * a + a2 * a) = 0 (-10a + 2a2 + a3) = 0 Solving -10a + 2a2 + a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-10 + 2a + a2) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-10 + 2a + a2)' equal to zero and attempt to solve: Simplifying -10 + 2a + a2 = 0 Solving -10 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 2a + 10 + a2 = 0 + 10 Reorder the terms: -10 + 10 + 2a + a2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2a + a2 = 0 + 10 2a + a2 = 0 + 10 Combine like terms: 0 + 10 = 10 2a + a2 = 10 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 10 + 1 Reorder the terms: 1 + 2a + a2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2a + a2 = 11 Factor a perfect square on the left side: (a + 1)(a + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (a + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
a + 1 = 3.31662479 Simplifying a + 1 = 3.31662479 Reorder the terms: 1 + a = 3.31662479 Solving 1 + a = 3.31662479 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + a = 3.31662479 + -1 a = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 a = 2.31662479 Simplifying a = 2.31662479Subproblem 2
a + 1 = -3.31662479 Simplifying a + 1 = -3.31662479 Reorder the terms: 1 + a = -3.31662479 Solving 1 + a = -3.31662479 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + a = -3.31662479 + -1 a = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 a = -4.31662479 Simplifying a = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.31662479, -4.31662479}Solution
a = {0, 2.31662479, -4.31662479}
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