4x^2+18x-20=10

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Solution for 4x^2+18x-20=10 equation: 


Simplifying
4x2 + 18x + -20 = 10

Reorder the terms:
-20 + 18x + 4x2 = 10

Solving
-20 + 18x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
-20 + -10 + 18x + 4x2 = 10 + -10

Combine like terms: -20 + -10 = -30
-30 + 18x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-30 + 18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 9x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + 9x + 2x2)' equal to zero and attempt to solve:

Simplifying
-15 + 9x + 2x2 = 0

Solving
-15 + 9x + 2x2 = 0

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

Divide each side by '2'.
-7.5 + 4.5x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 4.5x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 4.5x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 4.5x + x2 = 0 + 7.5
4.5x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
4.5x + x2 = 7.5

The x term is 4.5x.  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.
4.5x + 5.0625 + x2 = 7.5 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 7.5 + 5.0625

Combine like terms: 7.5 + 5.0625 = 12.5625
5.0625 + 4.5x + x2 = 12.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(x + 2.25) equal to 3.54436172 and -3.54436172.


Subproblem 1
x + 2.25 = 3.54436172

Simplifying
x + 2.25 = 3.54436172

Reorder the terms:
2.25 + x = 3.54436172

Solving
2.25 + x = 3.54436172

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 3.54436172 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 3.54436172 + -2.25
x = 3.54436172 + -2.25

Combine like terms: 3.54436172 + -2.25 = 1.29436172
x = 1.29436172

Simplifying
x = 1.29436172


Subproblem 2
x + 2.25 = -3.54436172

Simplifying
x + 2.25 = -3.54436172

Reorder the terms:
2.25 + x = -3.54436172

Solving
2.25 + x = -3.54436172

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -3.54436172 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -3.54436172 + -2.25
x = -3.54436172 + -2.25

Combine like terms: -3.54436172 + -2.25 = -5.79436172
x = -5.79436172

Simplifying
x = -5.79436172


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.29436172, -5.79436172}
Solution
x = {1.29436172, -5.79436172}

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