2x^2-48x=7x^2-4x-32

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Solution for 2x^2-48x=7x^2-4x-32 equation:


Simplifying
2x2 + -48x = 7x2 + -4x + -32

Reorder the terms:
-48x + 2x2 = 7x2 + -4x + -32

Reorder the terms:
-48x + 2x2 = -32 + -4x + 7x2

Solving
-48x + 2x2 = -32 + -4x + 7x2

Solving for variable 'x'.

Reorder the terms:
32 + -48x + 4x + 2x2 + -7x2 = -32 + -4x + 7x2 + 32 + 4x + -7x2

Combine like terms: -48x + 4x = -44x
32 + -44x + 2x2 + -7x2 = -32 + -4x + 7x2 + 32 + 4x + -7x2

Combine like terms: 2x2 + -7x2 = -5x2
32 + -44x + -5x2 = -32 + -4x + 7x2 + 32 + 4x + -7x2

Reorder the terms:
32 + -44x + -5x2 = -32 + 32 + -4x + 4x + 7x2 + -7x2

Combine like terms: -32 + 32 = 0
32 + -44x + -5x2 = 0 + -4x + 4x + 7x2 + -7x2
32 + -44x + -5x2 = -4x + 4x + 7x2 + -7x2

Combine like terms: -4x + 4x = 0
32 + -44x + -5x2 = 0 + 7x2 + -7x2
32 + -44x + -5x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
32 + -44x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-6.4 + 8.8x + x2 = 0

Move the constant term to the right:

Add '6.4' to each side of the equation.
-6.4 + 8.8x + 6.4 + x2 = 0 + 6.4

Reorder the terms:
-6.4 + 6.4 + 8.8x + x2 = 0 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + 8.8x + x2 = 0 + 6.4
8.8x + x2 = 0 + 6.4

Combine like terms: 0 + 6.4 = 6.4
8.8x + x2 = 6.4

The x term is 8.8x.  Take half its coefficient (4.4).
Square it (19.36) and add it to both sides.

Add '19.36' to each side of the equation.
8.8x + 19.36 + x2 = 6.4 + 19.36

Reorder the terms:
19.36 + 8.8x + x2 = 6.4 + 19.36

Combine like terms: 6.4 + 19.36 = 25.76
19.36 + 8.8x + x2 = 25.76

Factor a perfect square on the left side:
(x + 4.4)(x + 4.4) = 25.76

Calculate the square root of the right side: 5.075431016

Break this problem into two subproblems by setting 
(x + 4.4) equal to 5.075431016 and -5.075431016.

Subproblem 1

x + 4.4 = 5.075431016 Simplifying x + 4.4 = 5.075431016 Reorder the terms: 4.4 + x = 5.075431016 Solving 4.4 + x = 5.075431016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = 5.075431016 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = 5.075431016 + -4.4 x = 5.075431016 + -4.4 Combine like terms: 5.075431016 + -4.4 = 0.675431016 x = 0.675431016 Simplifying x = 0.675431016

Subproblem 2

x + 4.4 = -5.075431016 Simplifying x + 4.4 = -5.075431016 Reorder the terms: 4.4 + x = -5.075431016 Solving 4.4 + x = -5.075431016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = -5.075431016 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = -5.075431016 + -4.4 x = -5.075431016 + -4.4 Combine like terms: -5.075431016 + -4.4 = -9.475431016 x = -9.475431016 Simplifying x = -9.475431016

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.675431016, -9.475431016}

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