4x^2+22x-10=0

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Solution for 4x^2+22x-10=0 equation: 


Simplifying
4x2 + 22x + -10 = 0

Reorder the terms:
-10 + 22x + 4x2 = 0

Solving
-10 + 22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 11x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-5 + 11x + 2x2 = 0

Solving
-5 + 11x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + 5.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 5.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 5.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 5.5x + x2 = 0 + 2.5
5.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
5.5x + x2 = 2.5

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 2.5 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 2.5 + 7.5625

Combine like terms: 2.5 + 7.5625 = 10.0625
7.5625 + 5.5x + x2 = 10.0625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(x + 2.75) equal to 3.172144385 and -3.172144385.


Subproblem 1
x + 2.75 = 3.172144385

Simplifying
x + 2.75 = 3.172144385

Reorder the terms:
2.75 + x = 3.172144385

Solving
2.75 + x = 3.172144385

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 3.172144385 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 3.172144385 + -2.75
x = 3.172144385 + -2.75

Combine like terms: 3.172144385 + -2.75 = 0.422144385
x = 0.422144385

Simplifying
x = 0.422144385


Subproblem 2
x + 2.75 = -3.172144385

Simplifying
x + 2.75 = -3.172144385

Reorder the terms:
2.75 + x = -3.172144385

Solving
2.75 + x = -3.172144385

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -3.172144385 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -3.172144385 + -2.75
x = -3.172144385 + -2.75

Combine like terms: -3.172144385 + -2.75 = -5.922144385
x = -5.922144385

Simplifying
x = -5.922144385


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.422144385, -5.922144385}
Solution
x = {0.422144385, -5.922144385}

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