x^2-4=2x+7

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


Simplifying
x2 + -4 = 2x + 7

Reorder the terms:
-4 + x2 = 2x + 7

Reorder the terms:
-4 + x2 = 7 + 2x

Solving
-4 + x2 = 7 + 2x

Solving for variable 'x'.

Reorder the terms:
-4 + -7 + -2x + x2 = 7 + 2x + -7 + -2x

Combine like terms: -4 + -7 = -11
-11 + -2x + x2 = 7 + 2x + -7 + -2x

Reorder the terms:
-11 + -2x + x2 = 7 + -7 + 2x + -2x

Combine like terms: 7 + -7 = 0
-11 + -2x + x2 = 0 + 2x + -2x
-11 + -2x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-11 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -2x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -2x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2x + x2 = 0 + 11
-2x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-2x + x2 = 11

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 = 11 + 1

Reorder the terms:
1 + -2x + x2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + -2x + x2 = 12

Factor a perfect square on the left side:
(x + -1)(x + -1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -1) equal to 3.464101615 and -3.464101615.

Subproblem 1

x + -1 = 3.464101615 Simplifying x + -1 = 3.464101615 Reorder the terms: -1 + x = 3.464101615 Solving -1 + x = 3.464101615 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 = 3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.464101615 + 1 x = 3.464101615 + 1 Combine like terms: 3.464101615 + 1 = 4.464101615 x = 4.464101615 Simplifying x = 4.464101615

Subproblem 2

x + -1 = -3.464101615 Simplifying x + -1 = -3.464101615 Reorder the terms: -1 + x = -3.464101615 Solving -1 + x = -3.464101615 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 = -3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.464101615 + 1 x = -3.464101615 + 1 Combine like terms: -3.464101615 + 1 = -2.464101615 x = -2.464101615 Simplifying x = -2.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.464101615, -2.464101615}

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