2x^2+14x-4=x^2+3x

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Solution for 2x^2+14x-4=x^2+3x equation:


Simplifying
2x2 + 14x + -4 = x2 + 3x

Reorder the terms:
-4 + 14x + 2x2 = x2 + 3x

Reorder the terms:
-4 + 14x + 2x2 = 3x + x2

Solving
-4 + 14x + 2x2 = 3x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + 14x + -3x + 2x2 + -1x2 = 3x + x2 + -3x + -1x2

Combine like terms: 14x + -3x = 11x
-4 + 11x + 2x2 + -1x2 = 3x + x2 + -3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-4 + 11x + 1x2 = 3x + x2 + -3x + -1x2

Reorder the terms:
-4 + 11x + 1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-4 + 11x + 1x2 = 0 + x2 + -1x2
-4 + 11x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 11x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 11x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 11x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 11x + x2 = 0 + 4
11x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
11x + x2 = 4

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 4 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 4 + 30.25

Combine like terms: 4 + 30.25 = 34.25
30.25 + 11x + x2 = 34.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

x + 5.5 = 5.852349955 Simplifying x + 5.5 = 5.852349955 Reorder the terms: 5.5 + x = 5.852349955 Solving 5.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 5.852349955 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.852349955 + -5.5 x = 5.852349955 + -5.5 Combine like terms: 5.852349955 + -5.5 = 0.352349955 x = 0.352349955 Simplifying x = 0.352349955

Subproblem 2

x + 5.5 = -5.852349955 Simplifying x + 5.5 = -5.852349955 Reorder the terms: 5.5 + x = -5.852349955 Solving 5.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -5.852349955 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.852349955 + -5.5 x = -5.852349955 + -5.5 Combine like terms: -5.852349955 + -5.5 = -11.352349955 x = -11.352349955 Simplifying x = -11.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.352349955, -11.352349955}

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