2x^2+8x=3x+48

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Solution for 2x^2+8x=3x+48 equation:


Simplifying
2x2 + 8x = 3x + 48

Reorder the terms:
8x + 2x2 = 3x + 48

Reorder the terms:
8x + 2x2 = 48 + 3x

Solving
8x + 2x2 = 48 + 3x

Solving for variable 'x'.

Reorder the terms:
-48 + 8x + -3x + 2x2 = 48 + 3x + -48 + -3x

Combine like terms: 8x + -3x = 5x
-48 + 5x + 2x2 = 48 + 3x + -48 + -3x

Reorder the terms:
-48 + 5x + 2x2 = 48 + -48 + 3x + -3x

Combine like terms: 48 + -48 = 0
-48 + 5x + 2x2 = 0 + 3x + -3x
-48 + 5x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-48 + 5x + 2x2 = 0

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

Divide each side by '2'.
-24 + 2.5x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 2.5x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 2.5x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 2.5x + x2 = 0 + 24
2.5x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
2.5x + x2 = 24

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 24 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 24 + 1.5625

Combine like terms: 24 + 1.5625 = 25.5625
1.5625 + 2.5x + x2 = 25.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 25.5625

Calculate the square root of the right side: 5.055937104

Break this problem into two subproblems by setting 
(x + 1.25) equal to 5.055937104 and -5.055937104.

Subproblem 1

x + 1.25 = 5.055937104 Simplifying x + 1.25 = 5.055937104 Reorder the terms: 1.25 + x = 5.055937104 Solving 1.25 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 5.055937104 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 5.055937104 + -1.25 x = 5.055937104 + -1.25 Combine like terms: 5.055937104 + -1.25 = 3.805937104 x = 3.805937104 Simplifying x = 3.805937104

Subproblem 2

x + 1.25 = -5.055937104 Simplifying x + 1.25 = -5.055937104 Reorder the terms: 1.25 + x = -5.055937104 Solving 1.25 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -5.055937104 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -5.055937104 + -1.25 x = -5.055937104 + -1.25 Combine like terms: -5.055937104 + -1.25 = -6.305937104 x = -6.305937104 Simplifying x = -6.305937104

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.805937104, -6.305937104}

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