x^2+16x=21

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Solution for x^2+16x=21 equation:


Simplifying
x2 + 16x = 21

Reorder the terms:
16x + x2 = 21

Solving
16x + x2 = 21

Solving for variable 'x'.

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

Combine like terms: 21 + -21 = 0
-21 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 16x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 16x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 16x + x2 = 0 + 21
16x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
16x + x2 = 21

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 21 + 64

Reorder the terms:
64 + 16x + x2 = 21 + 64

Combine like terms: 21 + 64 = 85
64 + 16x + x2 = 85

Factor a perfect square on the left side:
(x + 8)(x + 8) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(x + 8) equal to 9.219544457 and -9.219544457.

Subproblem 1

x + 8 = 9.219544457 Simplifying x + 8 = 9.219544457 Reorder the terms: 8 + x = 9.219544457 Solving 8 + x = 9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 9.219544457 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.219544457 + -8 x = 9.219544457 + -8 Combine like terms: 9.219544457 + -8 = 1.219544457 x = 1.219544457 Simplifying x = 1.219544457

Subproblem 2

x + 8 = -9.219544457 Simplifying x + 8 = -9.219544457 Reorder the terms: 8 + x = -9.219544457 Solving 8 + x = -9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -9.219544457 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.219544457 + -8 x = -9.219544457 + -8 Combine like terms: -9.219544457 + -8 = -17.219544457 x = -17.219544457 Simplifying x = -17.219544457

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.219544457, -17.219544457}

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