x(2x-5)=196

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Solution for x(2x-5)=196 equation:


Simplifying
x(2x + -5) = 196

Reorder the terms:
x(-5 + 2x) = 196
(-5 * x + 2x * x) = 196
(-5x + 2x2) = 196

Solving
-5x + 2x2 = 196

Solving for variable 'x'.

Reorder the terms:
-196 + -5x + 2x2 = 196 + -196

Combine like terms: 196 + -196 = 0
-196 + -5x + 2x2 = 0

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

Divide each side by '2'.
-98 + -2.5x + x2 = 0

Move the constant term to the right:

Add '98' to each side of the equation.
-98 + -2.5x + 98 + x2 = 0 + 98

Reorder the terms:
-98 + 98 + -2.5x + x2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + -2.5x + x2 = 0 + 98
-2.5x + x2 = 0 + 98

Combine like terms: 0 + 98 = 98
-2.5x + x2 = 98

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 98 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 98 + 1.5625

Combine like terms: 98 + 1.5625 = 99.5625
1.5625 + -2.5x + x2 = 99.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 99.5625

Calculate the square root of the right side: 9.978101022

Break this problem into two subproblems by setting 
(x + -1.25) equal to 9.978101022 and -9.978101022.

Subproblem 1

x + -1.25 = 9.978101022 Simplifying x + -1.25 = 9.978101022 Reorder the terms: -1.25 + x = 9.978101022 Solving -1.25 + x = 9.978101022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 9.978101022 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 9.978101022 + 1.25 x = 9.978101022 + 1.25 Combine like terms: 9.978101022 + 1.25 = 11.228101022 x = 11.228101022 Simplifying x = 11.228101022

Subproblem 2

x + -1.25 = -9.978101022 Simplifying x + -1.25 = -9.978101022 Reorder the terms: -1.25 + x = -9.978101022 Solving -1.25 + x = -9.978101022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -9.978101022 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -9.978101022 + 1.25 x = -9.978101022 + 1.25 Combine like terms: -9.978101022 + 1.25 = -8.728101022 x = -8.728101022 Simplifying x = -8.728101022

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.228101022, -8.728101022}

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