x^2+20x=4x+30

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Solution for x^2+20x=4x+30 equation:


Simplifying
x2 + 20x = 4x + 30

Reorder the terms:
20x + x2 = 4x + 30

Reorder the terms:
20x + x2 = 30 + 4x

Solving
20x + x2 = 30 + 4x

Solving for variable 'x'.

Reorder the terms:
-30 + 20x + -4x + x2 = 30 + 4x + -30 + -4x

Combine like terms: 20x + -4x = 16x
-30 + 16x + x2 = 30 + 4x + -30 + -4x

Reorder the terms:
-30 + 16x + x2 = 30 + -30 + 4x + -4x

Combine like terms: 30 + -30 = 0
-30 + 16x + x2 = 0 + 4x + -4x
-30 + 16x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-30 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 16x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 16x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 16x + x2 = 0 + 30
16x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
16x + x2 = 30

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 = 30 + 64

Reorder the terms:
64 + 16x + x2 = 30 + 64

Combine like terms: 30 + 64 = 94
64 + 16x + x2 = 94

Factor a perfect square on the left side:
(x + 8)(x + 8) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(x + 8) equal to 9.695359715 and -9.695359715.

Subproblem 1

x + 8 = 9.695359715 Simplifying x + 8 = 9.695359715 Reorder the terms: 8 + x = 9.695359715 Solving 8 + x = 9.695359715 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 = 9.695359715 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.695359715 + -8 x = 9.695359715 + -8 Combine like terms: 9.695359715 + -8 = 1.695359715 x = 1.695359715 Simplifying x = 1.695359715

Subproblem 2

x + 8 = -9.695359715 Simplifying x + 8 = -9.695359715 Reorder the terms: 8 + x = -9.695359715 Solving 8 + x = -9.695359715 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 = -9.695359715 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.695359715 + -8 x = -9.695359715 + -8 Combine like terms: -9.695359715 + -8 = -17.695359715 x = -17.695359715 Simplifying x = -17.695359715

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.695359715, -17.695359715}

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