8x^2+46x-30=0

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Solution for 8x^2+46x-30=0 equation:


Simplifying
8x2 + 46x + -30 = 0

Reorder the terms:
-30 + 46x + 8x2 = 0

Solving
-30 + 46x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 23x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + 23x + 4x2)' equal to zero and attempt to solve:

Simplifying
-15 + 23x + 4x2 = 0

Solving
-15 + 23x + 4x2 = 0

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

Divide each side by '4'.
-3.75 + 5.75x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 5.75x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 5.75x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 5.75x + x2 = 0 + 3.75
5.75x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
5.75x + x2 = 3.75

The x term is 5.75x.  Take half its coefficient (2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
5.75x + 8.265625 + x2 = 3.75 + 8.265625

Reorder the terms:
8.265625 + 5.75x + x2 = 3.75 + 8.265625

Combine like terms: 3.75 + 8.265625 = 12.015625
8.265625 + 5.75x + x2 = 12.015625

Factor a perfect square on the left side:
(x + 2.875)(x + 2.875) = 12.015625

Calculate the square root of the right side: 3.466356156

Break this problem into two subproblems by setting 
(x + 2.875) equal to 3.466356156 and -3.466356156.


Subproblem 1
x + 2.875 = 3.466356156

Simplifying
x + 2.875 = 3.466356156

Reorder the terms:
2.875 + x = 3.466356156

Solving
2.875 + x = 3.466356156

Solving for variable 'x'.

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

Add '-2.875' to each side of the equation.
2.875 + -2.875 + x = 3.466356156 + -2.875

Combine like terms: 2.875 + -2.875 = 0.000
0.000 + x = 3.466356156 + -2.875
x = 3.466356156 + -2.875

Combine like terms: 3.466356156 + -2.875 = 0.591356156
x = 0.591356156

Simplifying
x = 0.591356156


Subproblem 2
x + 2.875 = -3.466356156

Simplifying
x + 2.875 = -3.466356156

Reorder the terms:
2.875 + x = -3.466356156

Solving
2.875 + x = -3.466356156

Solving for variable 'x'.

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

Add '-2.875' to each side of the equation.
2.875 + -2.875 + x = -3.466356156 + -2.875

Combine like terms: 2.875 + -2.875 = 0.000
0.000 + x = -3.466356156 + -2.875
x = -3.466356156 + -2.875

Combine like terms: -3.466356156 + -2.875 = -6.341356156
x = -6.341356156

Simplifying
x = -6.341356156


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.591356156, -6.341356156}
Solution
x = {0.591356156, -6.341356156}

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