3x^2-28=-2x^2-5x-24

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Solution for 3x^2-28=-2x^2-5x-24 equation:


Simplifying
3x2 + -28 = -2x2 + -5x + -24

Reorder the terms:
-28 + 3x2 = -2x2 + -5x + -24

Reorder the terms:
-28 + 3x2 = -24 + -5x + -2x2

Solving
-28 + 3x2 = -24 + -5x + -2x2

Solving for variable 'x'.

Reorder the terms:
-28 + 24 + 5x + 3x2 + 2x2 = -24 + -5x + -2x2 + 24 + 5x + 2x2

Combine like terms: -28 + 24 = -4
-4 + 5x + 3x2 + 2x2 = -24 + -5x + -2x2 + 24 + 5x + 2x2

Combine like terms: 3x2 + 2x2 = 5x2
-4 + 5x + 5x2 = -24 + -5x + -2x2 + 24 + 5x + 2x2

Reorder the terms:
-4 + 5x + 5x2 = -24 + 24 + -5x + 5x + -2x2 + 2x2

Combine like terms: -24 + 24 = 0
-4 + 5x + 5x2 = 0 + -5x + 5x + -2x2 + 2x2
-4 + 5x + 5x2 = -5x + 5x + -2x2 + 2x2

Combine like terms: -5x + 5x = 0
-4 + 5x + 5x2 = 0 + -2x2 + 2x2
-4 + 5x + 5x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-4 + 5x + 5x2 = 0

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

Divide each side by '5'.
-0.8 + x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x + x2 = 0 + 0.8
x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
x + x2 = 0.8

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.8 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.8 + 0.25

Combine like terms: 0.8 + 0.25 = 1.05
1.25 + x2 = 1.05

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.05

Calculate the square root of the right side: 1.024695077

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.024695077 and -1.024695077.

Subproblem 1

x + 0.5 = 1.024695077 Simplifying x + 0.5 = 1.024695077 Reorder the terms: 0.5 + x = 1.024695077 Solving 0.5 + x = 1.024695077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.024695077 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.024695077 + -0.5 x = 1.024695077 + -0.5 Combine like terms: 1.024695077 + -0.5 = 0.524695077 x = 0.524695077 Simplifying x = 0.524695077

Subproblem 2

x + 0.5 = -1.024695077 Simplifying x + 0.5 = -1.024695077 Reorder the terms: 0.5 + x = -1.024695077 Solving 0.5 + x = -1.024695077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.024695077 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.024695077 + -0.5 x = -1.024695077 + -0.5 Combine like terms: -1.024695077 + -0.5 = -1.524695077 x = -1.524695077 Simplifying x = -1.524695077

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.524695077, -1.524695077}

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