-2x^2+21=4x

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Solution for -2x^2+21=4x equation:


Simplifying
-2x2 + 21 = 4x

Reorder the terms:
21 + -2x2 = 4x

Solving
21 + -2x2 = 4x

Solving for variable 'x'.

Reorder the terms:
21 + -4x + -2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
21 + -4x + -2x2 = 0

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

Divide each side by '-2'.
-10.5 + 2x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + 2x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + 2x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + 2x + x2 = 0 + 10.5
2x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
2x + x2 = 10.5

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 = 10.5 + 1

Reorder the terms:
1 + 2x + x2 = 10.5 + 1

Combine like terms: 10.5 + 1 = 11.5
1 + 2x + x2 = 11.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 11.5

Calculate the square root of the right side: 3.391164992

Break this problem into two subproblems by setting 
(x + 1) equal to 3.391164992 and -3.391164992.

Subproblem 1

x + 1 = 3.391164992 Simplifying x + 1 = 3.391164992 Reorder the terms: 1 + x = 3.391164992 Solving 1 + x = 3.391164992 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 = 3.391164992 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.391164992 + -1 x = 3.391164992 + -1 Combine like terms: 3.391164992 + -1 = 2.391164992 x = 2.391164992 Simplifying x = 2.391164992

Subproblem 2

x + 1 = -3.391164992 Simplifying x + 1 = -3.391164992 Reorder the terms: 1 + x = -3.391164992 Solving 1 + x = -3.391164992 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 = -3.391164992 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.391164992 + -1 x = -3.391164992 + -1 Combine like terms: -3.391164992 + -1 = -4.391164992 x = -4.391164992 Simplifying x = -4.391164992

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.391164992, -4.391164992}

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