x^2=x+27

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Solution for x^2=x+27 equation:


Simplifying
x2 = x + 27

Reorder the terms:
x2 = 27 + x

Solving
x2 = 27 + x

Solving for variable 'x'.

Reorder the terms:
-27 + -1x + x2 = 27 + x + -27 + -1x

Reorder the terms:
-27 + -1x + x2 = 27 + -27 + x + -1x

Combine like terms: 27 + -27 = 0
-27 + -1x + x2 = 0 + x + -1x
-27 + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-27 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -1x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -1x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1x + x2 = 0 + 27
-1x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-1x + x2 = 27

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 27 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 27 + 0.25

Combine like terms: 27 + 0.25 = 27.25
0.25 + -1x + x2 = 27.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.220153254 and -5.220153254.

Subproblem 1

x + -0.5 = 5.220153254 Simplifying x + -0.5 = 5.220153254 Reorder the terms: -0.5 + x = 5.220153254 Solving -0.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.220153254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.220153254 + 0.5 x = 5.220153254 + 0.5 Combine like terms: 5.220153254 + 0.5 = 5.720153254 x = 5.720153254 Simplifying x = 5.720153254

Subproblem 2

x + -0.5 = -5.220153254 Simplifying x + -0.5 = -5.220153254 Reorder the terms: -0.5 + x = -5.220153254 Solving -0.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.220153254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.220153254 + 0.5 x = -5.220153254 + 0.5 Combine like terms: -5.220153254 + 0.5 = -4.720153254 x = -4.720153254 Simplifying x = -4.720153254

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.720153254, -4.720153254}

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