x^2-48+7x=0

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Solution for x^2-48+7x=0 equation:


Simplifying
x2 + -48 + 7x = 0

Reorder the terms:
-48 + 7x + x2 = 0

Solving
-48 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 7x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 7x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 7x + x2 = 0 + 48
7x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
7x + x2 = 48

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 = 48 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 48 + 12.25

Combine like terms: 48 + 12.25 = 60.25
12.25 + 7x + x2 = 60.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(x + 3.5) equal to 7.762087348 and -7.762087348.

Subproblem 1

x + 3.5 = 7.762087348 Simplifying x + 3.5 = 7.762087348 Reorder the terms: 3.5 + x = 7.762087348 Solving 3.5 + x = 7.762087348 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 = 7.762087348 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.762087348 + -3.5 x = 7.762087348 + -3.5 Combine like terms: 7.762087348 + -3.5 = 4.262087348 x = 4.262087348 Simplifying x = 4.262087348

Subproblem 2

x + 3.5 = -7.762087348 Simplifying x + 3.5 = -7.762087348 Reorder the terms: 3.5 + x = -7.762087348 Solving 3.5 + x = -7.762087348 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 = -7.762087348 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.762087348 + -3.5 x = -7.762087348 + -3.5 Combine like terms: -7.762087348 + -3.5 = -11.262087348 x = -11.262087348 Simplifying x = -11.262087348

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.262087348, -11.262087348}

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