7x^2+13x-25=0

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Solution for 7x^2+13x-25=0 equation:


Simplifying
7x2 + 13x + -25 = 0

Reorder the terms:
-25 + 13x + 7x2 = 0

Solving
-25 + 13x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-3.571428571 + 1.857142857x + x2 = 0

Move the constant term to the right:

Add '3.571428571' to each side of the equation.
-3.571428571 + 1.857142857x + 3.571428571 + x2 = 0 + 3.571428571

Reorder the terms:
-3.571428571 + 3.571428571 + 1.857142857x + x2 = 0 + 3.571428571

Combine like terms: -3.571428571 + 3.571428571 = 0.000000000
0.000000000 + 1.857142857x + x2 = 0 + 3.571428571
1.857142857x + x2 = 0 + 3.571428571

Combine like terms: 0 + 3.571428571 = 3.571428571
1.857142857x + x2 = 3.571428571

The x term is 1.857142857x.  Take half its coefficient (0.9285714285).
Square it (0.8622448978) and add it to both sides.

Add '0.8622448978' to each side of the equation.
1.857142857x + 0.8622448978 + x2 = 3.571428571 + 0.8622448978

Reorder the terms:
0.8622448978 + 1.857142857x + x2 = 3.571428571 + 0.8622448978

Combine like terms: 3.571428571 + 0.8622448978 = 4.4336734688
0.8622448978 + 1.857142857x + x2 = 4.4336734688

Factor a perfect square on the left side:
(x + 0.9285714285)(x + 0.9285714285) = 4.4336734688

Calculate the square root of the right side: 2.105628996

Break this problem into two subproblems by setting 
(x + 0.9285714285) equal to 2.105628996 and -2.105628996.

Subproblem 1

x + 0.9285714285 = 2.105628996 Simplifying x + 0.9285714285 = 2.105628996 Reorder the terms: 0.9285714285 + x = 2.105628996 Solving 0.9285714285 + x = 2.105628996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = 2.105628996 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = 2.105628996 + -0.9285714285 x = 2.105628996 + -0.9285714285 Combine like terms: 2.105628996 + -0.9285714285 = 1.1770575675 x = 1.1770575675 Simplifying x = 1.1770575675

Subproblem 2

x + 0.9285714285 = -2.105628996 Simplifying x + 0.9285714285 = -2.105628996 Reorder the terms: 0.9285714285 + x = -2.105628996 Solving 0.9285714285 + x = -2.105628996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = -2.105628996 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = -2.105628996 + -0.9285714285 x = -2.105628996 + -0.9285714285 Combine like terms: -2.105628996 + -0.9285714285 = -3.0342004245 x = -3.0342004245 Simplifying x = -3.0342004245

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1770575675, -3.0342004245}

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