x^2-8x=21

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Solution for x^2-8x=21 equation:


Simplifying
x2 + -8x = 21

Reorder the terms:
-8x + x2 = 21

Solving
-8x + x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + -8x + x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -8x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + -8x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -8x + x2 = 0 + 21
-8x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
-8x + x2 = 21

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 21 + 16

Reorder the terms:
16 + -8x + x2 = 21 + 16

Combine like terms: 21 + 16 = 37
16 + -8x + x2 = 37

Factor a perfect square on the left side:
(x + -4)(x + -4) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + -4) equal to 6.08276253 and -6.08276253.

Subproblem 1

x + -4 = 6.08276253 Simplifying x + -4 = 6.08276253 Reorder the terms: -4 + x = 6.08276253 Solving -4 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 6.08276253 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.08276253 + 4 x = 6.08276253 + 4 Combine like terms: 6.08276253 + 4 = 10.08276253 x = 10.08276253 Simplifying x = 10.08276253

Subproblem 2

x + -4 = -6.08276253 Simplifying x + -4 = -6.08276253 Reorder the terms: -4 + x = -6.08276253 Solving -4 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -6.08276253 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.08276253 + 4 x = -6.08276253 + 4 Combine like terms: -6.08276253 + 4 = -2.08276253 x = -2.08276253 Simplifying x = -2.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.08276253, -2.08276253}

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