4x^2+5x-10=0

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Solution for 4x^2+5x-10=0 equation: 


Simplifying
4x2 + 5x + -10 = 0

Reorder the terms:
-10 + 5x + 4x2 = 0

Solving
-10 + 5x + 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 + 1.25x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 1.25x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 1.25x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 1.25x + x2 = 0 + 2.5
1.25x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
1.25x + x2 = 2.5

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 2.5 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 2.5 + 0.390625

Combine like terms: 2.5 + 0.390625 = 2.890625
0.390625 + 1.25x + x2 = 2.890625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 2.890625

Calculate the square root of the right side: 1.700183814

Break this problem into two subproblems by setting 
(x + 0.625) equal to 1.700183814 and -1.700183814.


Subproblem 1
x + 0.625 = 1.700183814

Simplifying
x + 0.625 = 1.700183814

Reorder the terms:
0.625 + x = 1.700183814

Solving
0.625 + x = 1.700183814

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 1.700183814 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 1.700183814 + -0.625
x = 1.700183814 + -0.625

Combine like terms: 1.700183814 + -0.625 = 1.075183814
x = 1.075183814

Simplifying
x = 1.075183814


Subproblem 2
x + 0.625 = -1.700183814

Simplifying
x + 0.625 = -1.700183814

Reorder the terms:
0.625 + x = -1.700183814

Solving
0.625 + x = -1.700183814

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -1.700183814 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -1.700183814 + -0.625
x = -1.700183814 + -0.625

Combine like terms: -1.700183814 + -0.625 = -2.325183814
x = -2.325183814

Simplifying
x = -2.325183814


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.075183814, -2.325183814}

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