x^2+17x+21x=4x-1

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Solution for x^2+17x+21x=4x-1 equation:


Simplifying
x2 + 17x + 21x = 4x + -1

Reorder the terms:
17x + 21x + x2 = 4x + -1

Combine like terms: 17x + 21x = 38x
38x + x2 = 4x + -1

Reorder the terms:
38x + x2 = -1 + 4x

Solving
38x + x2 = -1 + 4x

Solving for variable 'x'.

Reorder the terms:
1 + 38x + -4x + x2 = -1 + 4x + 1 + -4x

Combine like terms: 38x + -4x = 34x
1 + 34x + x2 = -1 + 4x + 1 + -4x

Reorder the terms:
1 + 34x + x2 = -1 + 1 + 4x + -4x

Combine like terms: -1 + 1 = 0
1 + 34x + x2 = 0 + 4x + -4x
1 + 34x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
1 + 34x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 34x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 34x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 34x + x2 = 0 + -1
34x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
34x + x2 = -1

The x term is 34x.  Take half its coefficient (17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
34x + 289 + x2 = -1 + 289

Reorder the terms:
289 + 34x + x2 = -1 + 289

Combine like terms: -1 + 289 = 288
289 + 34x + x2 = 288

Factor a perfect square on the left side:
(x + 17)(x + 17) = 288

Calculate the square root of the right side: 16.970562748

Break this problem into two subproblems by setting 
(x + 17) equal to 16.970562748 and -16.970562748.

Subproblem 1

x + 17 = 16.970562748 Simplifying x + 17 = 16.970562748 Reorder the terms: 17 + x = 16.970562748 Solving 17 + x = 16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 16.970562748 + -17 Combine like terms: 17 + -17 = 0 0 + x = 16.970562748 + -17 x = 16.970562748 + -17 Combine like terms: 16.970562748 + -17 = -0.029437252 x = -0.029437252 Simplifying x = -0.029437252

Subproblem 2

x + 17 = -16.970562748 Simplifying x + 17 = -16.970562748 Reorder the terms: 17 + x = -16.970562748 Solving 17 + x = -16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -16.970562748 + -17 Combine like terms: 17 + -17 = 0 0 + x = -16.970562748 + -17 x = -16.970562748 + -17 Combine like terms: -16.970562748 + -17 = -33.970562748 x = -33.970562748 Simplifying x = -33.970562748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.029437252, -33.970562748}

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