2x^2+4x-25=0

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Solution for 2x^2+4x-25=0 equation:


Simplifying
2x2 + 4x + -25 = 0

Reorder the terms:
-25 + 4x + 2x2 = 0

Solving
-25 + 4x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-12.5 + 2x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 2x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 2x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 2x + x2 = 0 + 12.5
2x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
2x + x2 = 12.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 12.5 + 1

Reorder the terms:
1 + 2x + x2 = 12.5 + 1

Combine like terms: 12.5 + 1 = 13.5
1 + 2x + x2 = 13.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 13.5

Calculate the square root of the right side: 3.674234614

Break this problem into two subproblems by setting 
(x + 1) equal to 3.674234614 and -3.674234614.

Subproblem 1

x + 1 = 3.674234614 Simplifying x + 1 = 3.674234614 Reorder the terms: 1 + x = 3.674234614 Solving 1 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.674234614 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.674234614 + -1 x = 3.674234614 + -1 Combine like terms: 3.674234614 + -1 = 2.674234614 x = 2.674234614 Simplifying x = 2.674234614

Subproblem 2

x + 1 = -3.674234614 Simplifying x + 1 = -3.674234614 Reorder the terms: 1 + x = -3.674234614 Solving 1 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.674234614 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.674234614 + -1 x = -3.674234614 + -1 Combine like terms: -3.674234614 + -1 = -4.674234614 x = -4.674234614 Simplifying x = -4.674234614

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.674234614, -4.674234614}

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