25x^2+110x-278=0

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Solution for 25x^2+110x-278=0 equation:


Simplifying
25x2 + 110x + -278 = 0

Reorder the terms:
-278 + 110x + 25x2 = 0

Solving
-278 + 110x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
-11.12 + 4.4x + x2 = 0

Move the constant term to the right:

Add '11.12' to each side of the equation.
-11.12 + 4.4x + 11.12 + x2 = 0 + 11.12

Reorder the terms:
-11.12 + 11.12 + 4.4x + x2 = 0 + 11.12

Combine like terms: -11.12 + 11.12 = 0.00
0.00 + 4.4x + x2 = 0 + 11.12
4.4x + x2 = 0 + 11.12

Combine like terms: 0 + 11.12 = 11.12
4.4x + x2 = 11.12

The x term is 4.4x.  Take half its coefficient (2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
4.4x + 4.84 + x2 = 11.12 + 4.84

Reorder the terms:
4.84 + 4.4x + x2 = 11.12 + 4.84

Combine like terms: 11.12 + 4.84 = 15.96
4.84 + 4.4x + x2 = 15.96

Factor a perfect square on the left side:
(x + 2.2)(x + 2.2) = 15.96

Calculate the square root of the right side: 3.994996871

Break this problem into two subproblems by setting 
(x + 2.2) equal to 3.994996871 and -3.994996871.

Subproblem 1

x + 2.2 = 3.994996871 Simplifying x + 2.2 = 3.994996871 Reorder the terms: 2.2 + x = 3.994996871 Solving 2.2 + x = 3.994996871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = 3.994996871 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 3.994996871 + -2.2 x = 3.994996871 + -2.2 Combine like terms: 3.994996871 + -2.2 = 1.794996871 x = 1.794996871 Simplifying x = 1.794996871

Subproblem 2

x + 2.2 = -3.994996871 Simplifying x + 2.2 = -3.994996871 Reorder the terms: 2.2 + x = -3.994996871 Solving 2.2 + x = -3.994996871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = -3.994996871 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -3.994996871 + -2.2 x = -3.994996871 + -2.2 Combine like terms: -3.994996871 + -2.2 = -6.194996871 x = -6.194996871 Simplifying x = -6.194996871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.794996871, -6.194996871}

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