x^2-7x=5

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Solution for x^2-7x=5 equation:


Simplifying
x2 + -7x = 5

Reorder the terms:
-7x + x2 = 5

Solving
-7x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -7x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -7x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -7x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7x + x2 = 0 + 5
-7x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-7x + x2 = 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 = 5 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 5 + 12.25

Combine like terms: 5 + 12.25 = 17.25
12.25 + -7x + x2 = 17.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.153311931 and -4.153311931.

Subproblem 1

x + -3.5 = 4.153311931 Simplifying x + -3.5 = 4.153311931 Reorder the terms: -3.5 + x = 4.153311931 Solving -3.5 + x = 4.153311931 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 = 4.153311931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.153311931 + 3.5 x = 4.153311931 + 3.5 Combine like terms: 4.153311931 + 3.5 = 7.653311931 x = 7.653311931 Simplifying x = 7.653311931

Subproblem 2

x + -3.5 = -4.153311931 Simplifying x + -3.5 = -4.153311931 Reorder the terms: -3.5 + x = -4.153311931 Solving -3.5 + x = -4.153311931 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 = -4.153311931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.153311931 + 3.5 x = -4.153311931 + 3.5 Combine like terms: -4.153311931 + 3.5 = -0.653311931 x = -0.653311931 Simplifying x = -0.653311931

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.653311931, -0.653311931}

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