4a^2-18a+15=0

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Solution for 4a^2-18a+15=0 equation:


Simplifying
4a2 + -18a + 15 = 0

Reorder the terms:
15 + -18a + 4a2 = 0

Solving
15 + -18a + 4a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
3.75 + -4.5a + a2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -4.5a + -3.75 + a2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -4.5a + a2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -4.5a + a2 = 0 + -3.75
-4.5a + a2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-4.5a + a2 = -3.75

The a term is -4.5a.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5a + 5.0625 + a2 = -3.75 + 5.0625

Reorder the terms:
5.0625 + -4.5a + a2 = -3.75 + 5.0625

Combine like terms: -3.75 + 5.0625 = 1.3125
5.0625 + -4.5a + a2 = 1.3125

Factor a perfect square on the left side:
(a + -2.25)(a + -2.25) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(a + -2.25) equal to 1.145643924 and -1.145643924.

Subproblem 1

a + -2.25 = 1.145643924 Simplifying a + -2.25 = 1.145643924 Reorder the terms: -2.25 + a = 1.145643924 Solving -2.25 + a = 1.145643924 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + a = 1.145643924 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + a = 1.145643924 + 2.25 a = 1.145643924 + 2.25 Combine like terms: 1.145643924 + 2.25 = 3.395643924 a = 3.395643924 Simplifying a = 3.395643924

Subproblem 2

a + -2.25 = -1.145643924 Simplifying a + -2.25 = -1.145643924 Reorder the terms: -2.25 + a = -1.145643924 Solving -2.25 + a = -1.145643924 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + a = -1.145643924 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + a = -1.145643924 + 2.25 a = -1.145643924 + 2.25 Combine like terms: -1.145643924 + 2.25 = 1.104356076 a = 1.104356076 Simplifying a = 1.104356076

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.395643924, 1.104356076}

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