x*x+7x=14

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Solution for x*x+7x=14 equation:


Simplifying
x * x + 7x = 14

Multiply x * x
x2 + 7x = 14

Reorder the terms:
7x + x2 = 14

Solving
7x + x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 7x + x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 7x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 7x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 7x + x2 = 0 + 14
7x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
7x + x2 = 14

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 = 14 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 14 + 12.25

Combine like terms: 14 + 12.25 = 26.25
12.25 + 7x + x2 = 26.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.123475383 and -5.123475383.

Subproblem 1

x + 3.5 = 5.123475383 Simplifying x + 3.5 = 5.123475383 Reorder the terms: 3.5 + x = 5.123475383 Solving 3.5 + x = 5.123475383 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 = 5.123475383 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.123475383 + -3.5 x = 5.123475383 + -3.5 Combine like terms: 5.123475383 + -3.5 = 1.623475383 x = 1.623475383 Simplifying x = 1.623475383

Subproblem 2

x + 3.5 = -5.123475383 Simplifying x + 3.5 = -5.123475383 Reorder the terms: 3.5 + x = -5.123475383 Solving 3.5 + x = -5.123475383 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 = -5.123475383 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.123475383 + -3.5 x = -5.123475383 + -3.5 Combine like terms: -5.123475383 + -3.5 = -8.623475383 x = -8.623475383 Simplifying x = -8.623475383

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.623475383, -8.623475383}

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