2a^2-12a+18=14

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Solution for 2a^2-12a+18=14 equation:


Simplifying
2a2 + -12a + 18 = 14

Reorder the terms:
18 + -12a + 2a2 = 14

Solving
18 + -12a + 2a2 = 14

Solving for variable 'a'.

Reorder the terms:
18 + -14 + -12a + 2a2 = 14 + -14

Combine like terms: 18 + -14 = 4
4 + -12a + 2a2 = 14 + -14

Combine like terms: 14 + -14 = 0
4 + -12a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -6a + a2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + -6a + a2)' equal to zero and attempt to solve: Simplifying 2 + -6a + a2 = 0 Solving 2 + -6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6a + -2 + a2 = 0 + -2 Reorder the terms: 2 + -2 + -6a + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6a + a2 = 0 + -2 -6a + a2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6a + a2 = -2 The a term is -6a. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a + 9 + a2 = -2 + 9 Reorder the terms: 9 + -6a + a2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6a + a2 = 7 Factor a perfect square on the left side: (a + -3)(a + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (a + -3) equal to 2.645751311 and -2.645751311.

Subproblem 1

a + -3 = 2.645751311 Simplifying a + -3 = 2.645751311 Reorder the terms: -3 + a = 2.645751311 Solving -3 + a = 2.645751311 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + a = 2.645751311 + 3 a = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 a = 5.645751311 Simplifying a = 5.645751311

Subproblem 2

a + -3 = -2.645751311 Simplifying a + -3 = -2.645751311 Reorder the terms: -3 + a = -2.645751311 Solving -3 + a = -2.645751311 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + a = -2.645751311 + 3 a = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 a = 0.354248689 Simplifying a = 0.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.645751311, 0.354248689}

Solution

a = {5.645751311, 0.354248689}

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