4x+7=2x^2

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Solution for 4x+7=2x^2 equation:


Simplifying
4x + 7 = 2x2

Reorder the terms:
7 + 4x = 2x2

Solving
7 + 4x = 2x2

Solving for variable 'x'.

Combine like terms: 2x2 + -2x2 = 0
7 + 4x + -2x2 = 0

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

Divide each side by '-2'.
-3.5 + -2x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -2x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -2x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -2x + x2 = 0 + 3.5
-2x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-2x + x2 = 3.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 3.5 + 1

Reorder the terms:
1 + -2x + x2 = 3.5 + 1

Combine like terms: 3.5 + 1 = 4.5
1 + -2x + x2 = 4.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + -1) equal to 2.121320344 and -2.121320344.

Subproblem 1

x + -1 = 2.121320344 Simplifying x + -1 = 2.121320344 Reorder the terms: -1 + x = 2.121320344 Solving -1 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.121320344 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.121320344 + 1 x = 2.121320344 + 1 Combine like terms: 2.121320344 + 1 = 3.121320344 x = 3.121320344 Simplifying x = 3.121320344

Subproblem 2

x + -1 = -2.121320344 Simplifying x + -1 = -2.121320344 Reorder the terms: -1 + x = -2.121320344 Solving -1 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.121320344 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.121320344 + 1 x = -2.121320344 + 1 Combine like terms: -2.121320344 + 1 = -1.121320344 x = -1.121320344 Simplifying x = -1.121320344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.121320344, -1.121320344}

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