4x^2+15x-10=0

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Solution for 4x^2+15x-10=0 equation: 


Simplifying
4x2 + 15x + -10 = 0

Reorder the terms:
-10 + 15x + 4x2 = 0

Solving
-10 + 15x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-2.5 + 3.75x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 3.75x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 3.75x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 3.75x + x2 = 0 + 2.5
3.75x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
3.75x + x2 = 2.5

The x term is 3.75x.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75x + 3.515625 + x2 = 2.5 + 3.515625

Reorder the terms:
3.515625 + 3.75x + x2 = 2.5 + 3.515625

Combine like terms: 2.5 + 3.515625 = 6.015625
3.515625 + 3.75x + x2 = 6.015625

Factor a perfect square on the left side:
(x + 1.875)(x + 1.875) = 6.015625

Calculate the square root of the right side: 2.452677109

Break this problem into two subproblems by setting 
(x + 1.875) equal to 2.452677109 and -2.452677109.


Subproblem 1
x + 1.875 = 2.452677109

Simplifying
x + 1.875 = 2.452677109

Reorder the terms:
1.875 + x = 2.452677109

Solving
1.875 + x = 2.452677109

Solving for variable 'x'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + x = 2.452677109 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + x = 2.452677109 + -1.875
x = 2.452677109 + -1.875

Combine like terms: 2.452677109 + -1.875 = 0.577677109
x = 0.577677109

Simplifying
x = 0.577677109


Subproblem 2
x + 1.875 = -2.452677109

Simplifying
x + 1.875 = -2.452677109

Reorder the terms:
1.875 + x = -2.452677109

Solving
1.875 + x = -2.452677109

Solving for variable 'x'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + x = -2.452677109 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + x = -2.452677109 + -1.875
x = -2.452677109 + -1.875

Combine like terms: -2.452677109 + -1.875 = -4.327677109
x = -4.327677109

Simplifying
x = -4.327677109


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.577677109, -4.327677109}

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