2x(x+7)=25

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Solution for 2x(x+7)=25 equation:


Simplifying
2x(x + 7) = 25

Reorder the terms:
2x(7 + x) = 25
(7 * 2x + x * 2x) = 25
(14x + 2x2) = 25

Solving
14x + 2x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 14x + 2x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 14x + 2x2 = 0

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

Divide each side by '2'.
-12.5 + 7x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 7x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 7x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 7x + x2 = 0 + 12.5
7x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
7x + x2 = 12.5

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 12.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 12.5 + 12.25

Combine like terms: 12.5 + 12.25 = 24.75
12.25 + 7x + x2 = 24.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 24.75

Calculate the square root of the right side: 4.974937186

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.974937186 and -4.974937186.

Subproblem 1

x + 3.5 = 4.974937186 Simplifying x + 3.5 = 4.974937186 Reorder the terms: 3.5 + x = 4.974937186 Solving 3.5 + x = 4.974937186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.974937186 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.974937186 + -3.5 x = 4.974937186 + -3.5 Combine like terms: 4.974937186 + -3.5 = 1.474937186 x = 1.474937186 Simplifying x = 1.474937186

Subproblem 2

x + 3.5 = -4.974937186 Simplifying x + 3.5 = -4.974937186 Reorder the terms: 3.5 + x = -4.974937186 Solving 3.5 + x = -4.974937186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.974937186 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.974937186 + -3.5 x = -4.974937186 + -3.5 Combine like terms: -4.974937186 + -3.5 = -8.474937186 x = -8.474937186 Simplifying x = -8.474937186

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.474937186, -8.474937186}

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