a^2-30a+150=0

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Solution for a^2-30a+150=0 equation:


Simplifying
a2 + -30a + 150 = 0

Reorder the terms:
150 + -30a + a2 = 0

Solving
150 + -30a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-150' to each side of the equation.
150 + -30a + -150 + a2 = 0 + -150

Reorder the terms:
150 + -150 + -30a + a2 = 0 + -150

Combine like terms: 150 + -150 = 0
0 + -30a + a2 = 0 + -150
-30a + a2 = 0 + -150

Combine like terms: 0 + -150 = -150
-30a + a2 = -150

The a term is -30a.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30a + 225 + a2 = -150 + 225

Reorder the terms:
225 + -30a + a2 = -150 + 225

Combine like terms: -150 + 225 = 75
225 + -30a + a2 = 75

Factor a perfect square on the left side:
(a + -15)(a + -15) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(a + -15) equal to 8.660254038 and -8.660254038.

Subproblem 1

a + -15 = 8.660254038 Simplifying a + -15 = 8.660254038 Reorder the terms: -15 + a = 8.660254038 Solving -15 + a = 8.660254038 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + a = 8.660254038 + 15 Combine like terms: -15 + 15 = 0 0 + a = 8.660254038 + 15 a = 8.660254038 + 15 Combine like terms: 8.660254038 + 15 = 23.660254038 a = 23.660254038 Simplifying a = 23.660254038

Subproblem 2

a + -15 = -8.660254038 Simplifying a + -15 = -8.660254038 Reorder the terms: -15 + a = -8.660254038 Solving -15 + a = -8.660254038 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + a = -8.660254038 + 15 Combine like terms: -15 + 15 = 0 0 + a = -8.660254038 + 15 a = -8.660254038 + 15 Combine like terms: -8.660254038 + 15 = 6.339745962 a = 6.339745962 Simplifying a = 6.339745962

Solution

The solution to the problem is based on the solutions from the subproblems. a = {23.660254038, 6.339745962}

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