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Simplifying 2a2 + -14a + 18 = 0 Reorder the terms: 18 + -14a + 2a2 = 0 Solving 18 + -14a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -7a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -7a + a2)' equal to zero and attempt to solve: Simplifying 9 + -7a + a2 = 0 Solving 9 + -7a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -7a + -9 + a2 = 0 + -9 Reorder the terms: 9 + -9 + -7a + a2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7a + a2 = 0 + -9 -7a + a2 = 0 + -9 Combine like terms: 0 + -9 = -9 -7a + a2 = -9 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 = -9 + 12.25 Reorder the terms: 12.25 + -7a + a2 = -9 + 12.25 Combine like terms: -9 + 12.25 = 3.25 12.25 + -7a + a2 = 3.25 Factor a perfect square on the left side: (a + -3.5)(a + -3.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (a + -3.5) equal to 1.802775638 and -1.802775638.Subproblem 1
a + -3.5 = 1.802775638 Simplifying a + -3.5 = 1.802775638 Reorder the terms: -3.5 + a = 1.802775638 Solving -3.5 + a = 1.802775638 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 = 1.802775638 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 1.802775638 + 3.5 a = 1.802775638 + 3.5 Combine like terms: 1.802775638 + 3.5 = 5.302775638 a = 5.302775638 Simplifying a = 5.302775638Subproblem 2
a + -3.5 = -1.802775638 Simplifying a + -3.5 = -1.802775638 Reorder the terms: -3.5 + a = -1.802775638 Solving -3.5 + a = -1.802775638 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 = -1.802775638 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -1.802775638 + 3.5 a = -1.802775638 + 3.5 Combine like terms: -1.802775638 + 3.5 = 1.697224362 a = 1.697224362 Simplifying a = 1.697224362Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.302775638, 1.697224362}Solution
a = {5.302775638, 1.697224362}
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