x^2+28x-34=0

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Solution for x^2+28x-34=0 equation:


Simplifying
x2 + 28x + -34 = 0

Reorder the terms:
-34 + 28x + x2 = 0

Solving
-34 + 28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 28x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + 28x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 28x + x2 = 0 + 34
28x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
28x + x2 = 34

The x term is 28x.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28x + 196 + x2 = 34 + 196

Reorder the terms:
196 + 28x + x2 = 34 + 196

Combine like terms: 34 + 196 = 230
196 + 28x + x2 = 230

Factor a perfect square on the left side:
(x + 14)(x + 14) = 230

Calculate the square root of the right side: 15.165750888

Break this problem into two subproblems by setting 
(x + 14) equal to 15.165750888 and -15.165750888.

Subproblem 1

x + 14 = 15.165750888 Simplifying x + 14 = 15.165750888 Reorder the terms: 14 + x = 15.165750888 Solving 14 + x = 15.165750888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 15.165750888 + -14 Combine like terms: 14 + -14 = 0 0 + x = 15.165750888 + -14 x = 15.165750888 + -14 Combine like terms: 15.165750888 + -14 = 1.165750888 x = 1.165750888 Simplifying x = 1.165750888

Subproblem 2

x + 14 = -15.165750888 Simplifying x + 14 = -15.165750888 Reorder the terms: 14 + x = -15.165750888 Solving 14 + x = -15.165750888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -15.165750888 + -14 Combine like terms: 14 + -14 = 0 0 + x = -15.165750888 + -14 x = -15.165750888 + -14 Combine like terms: -15.165750888 + -14 = -29.165750888 x = -29.165750888 Simplifying x = -29.165750888

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.165750888, -29.165750888}

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