3x^2-46=-4x^2-5x-30

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Solution for 3x^2-46=-4x^2-5x-30 equation:


Simplifying
3x2 + -46 = -4x2 + -5x + -30

Reorder the terms:
-46 + 3x2 = -4x2 + -5x + -30

Reorder the terms:
-46 + 3x2 = -30 + -5x + -4x2

Solving
-46 + 3x2 = -30 + -5x + -4x2

Solving for variable 'x'.

Reorder the terms:
-46 + 30 + 5x + 3x2 + 4x2 = -30 + -5x + -4x2 + 30 + 5x + 4x2

Combine like terms: -46 + 30 = -16
-16 + 5x + 3x2 + 4x2 = -30 + -5x + -4x2 + 30 + 5x + 4x2

Combine like terms: 3x2 + 4x2 = 7x2
-16 + 5x + 7x2 = -30 + -5x + -4x2 + 30 + 5x + 4x2

Reorder the terms:
-16 + 5x + 7x2 = -30 + 30 + -5x + 5x + -4x2 + 4x2

Combine like terms: -30 + 30 = 0
-16 + 5x + 7x2 = 0 + -5x + 5x + -4x2 + 4x2
-16 + 5x + 7x2 = -5x + 5x + -4x2 + 4x2

Combine like terms: -5x + 5x = 0
-16 + 5x + 7x2 = 0 + -4x2 + 4x2
-16 + 5x + 7x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-16 + 5x + 7x2 = 0

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

Divide each side by '7'.
-2.285714286 + 0.7142857143x + x2 = 0

Move the constant term to the right:

Add '2.285714286' to each side of the equation.
-2.285714286 + 0.7142857143x + 2.285714286 + x2 = 0 + 2.285714286

Reorder the terms:
-2.285714286 + 2.285714286 + 0.7142857143x + x2 = 0 + 2.285714286

Combine like terms: -2.285714286 + 2.285714286 = 0.000000000
0.000000000 + 0.7142857143x + x2 = 0 + 2.285714286
0.7142857143x + x2 = 0 + 2.285714286

Combine like terms: 0 + 2.285714286 = 2.285714286
0.7142857143x + x2 = 2.285714286

The x term is 0.7142857143x.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143x + 0.1275510204 + x2 = 2.285714286 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143x + x2 = 2.285714286 + 0.1275510204

Combine like terms: 2.285714286 + 0.1275510204 = 2.4132653064
0.1275510204 + 0.7142857143x + x2 = 2.4132653064

Factor a perfect square on the left side:
(x + 0.3571428572)(x + 0.3571428572) = 2.4132653064

Calculate the square root of the right side: 1.553468798

Break this problem into two subproblems by setting 
(x + 0.3571428572) equal to 1.553468798 and -1.553468798.

Subproblem 1

x + 0.3571428572 = 1.553468798 Simplifying x + 0.3571428572 = 1.553468798 Reorder the terms: 0.3571428572 + x = 1.553468798 Solving 0.3571428572 + x = 1.553468798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 1.553468798 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 1.553468798 + -0.3571428572 x = 1.553468798 + -0.3571428572 Combine like terms: 1.553468798 + -0.3571428572 = 1.1963259408 x = 1.1963259408 Simplifying x = 1.1963259408

Subproblem 2

x + 0.3571428572 = -1.553468798 Simplifying x + 0.3571428572 = -1.553468798 Reorder the terms: 0.3571428572 + x = -1.553468798 Solving 0.3571428572 + x = -1.553468798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -1.553468798 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -1.553468798 + -0.3571428572 x = -1.553468798 + -0.3571428572 Combine like terms: -1.553468798 + -0.3571428572 = -1.9106116552 x = -1.9106116552 Simplifying x = -1.9106116552

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1963259408, -1.9106116552}

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