x^2+10x=4x+21

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Solution for x^2+10x=4x+21 equation:


Simplifying
x2 + 10x = 4x + 21

Reorder the terms:
10x + x2 = 4x + 21

Reorder the terms:
10x + x2 = 21 + 4x

Solving
10x + x2 = 21 + 4x

Solving for variable 'x'.

Reorder the terms:
-21 + 10x + -4x + x2 = 21 + 4x + -21 + -4x

Combine like terms: 10x + -4x = 6x
-21 + 6x + x2 = 21 + 4x + -21 + -4x

Reorder the terms:
-21 + 6x + x2 = 21 + -21 + 4x + -4x

Combine like terms: 21 + -21 = 0
-21 + 6x + x2 = 0 + 4x + -4x
-21 + 6x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-21 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 6x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 6x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 6x + x2 = 0 + 21
6x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
6x + x2 = 21

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 21 + 9

Reorder the terms:
9 + 6x + x2 = 21 + 9

Combine like terms: 21 + 9 = 30
9 + 6x + x2 = 30

Factor a perfect square on the left side:
(x + 3)(x + 3) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + 3) equal to 5.477225575 and -5.477225575.

Subproblem 1

x + 3 = 5.477225575 Simplifying x + 3 = 5.477225575 Reorder the terms: 3 + x = 5.477225575 Solving 3 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.477225575 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.477225575 + -3 x = 5.477225575 + -3 Combine like terms: 5.477225575 + -3 = 2.477225575 x = 2.477225575 Simplifying x = 2.477225575

Subproblem 2

x + 3 = -5.477225575 Simplifying x + 3 = -5.477225575 Reorder the terms: 3 + x = -5.477225575 Solving 3 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.477225575 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.477225575 + -3 x = -5.477225575 + -3 Combine like terms: -5.477225575 + -3 = -8.477225575 x = -8.477225575 Simplifying x = -8.477225575

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.477225575, -8.477225575}

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