x^2+5x-3=26

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Solution for x^2+5x-3=26 equation:


Simplifying
x2 + 5x + -3 = 26

Reorder the terms:
-3 + 5x + x2 = 26

Solving
-3 + 5x + x2 = 26

Solving for variable 'x'.

Reorder the terms:
-3 + -26 + 5x + x2 = 26 + -26

Combine like terms: -3 + -26 = -29
-29 + 5x + x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-29 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 5x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 5x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 5x + x2 = 0 + 29
5x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
5x + x2 = 29

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 29 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 29 + 6.25

Combine like terms: 29 + 6.25 = 35.25
6.25 + 5x + x2 = 35.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.937171044 and -5.937171044.

Subproblem 1

x + 2.5 = 5.937171044 Simplifying x + 2.5 = 5.937171044 Reorder the terms: 2.5 + x = 5.937171044 Solving 2.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5.937171044 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.937171044 + -2.5 x = 5.937171044 + -2.5 Combine like terms: 5.937171044 + -2.5 = 3.437171044 x = 3.437171044 Simplifying x = 3.437171044

Subproblem 2

x + 2.5 = -5.937171044 Simplifying x + 2.5 = -5.937171044 Reorder the terms: 2.5 + x = -5.937171044 Solving 2.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5.937171044 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.937171044 + -2.5 x = -5.937171044 + -2.5 Combine like terms: -5.937171044 + -2.5 = -8.437171044 x = -8.437171044 Simplifying x = -8.437171044

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.437171044, -8.437171044}

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