x^2+28x-50=0

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Solution for x^2+28x-50=0 equation:


Simplifying
x2 + 28x + -50 = 0

Reorder the terms:
-50 + 28x + x2 = 0

Solving
-50 + 28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 28x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 28x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 28x + x2 = 0 + 50
28x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
28x + x2 = 50

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 = 50 + 196

Reorder the terms:
196 + 28x + x2 = 50 + 196

Combine like terms: 50 + 196 = 246
196 + 28x + x2 = 246

Factor a perfect square on the left side:
(x + 14)(x + 14) = 246

Calculate the square root of the right side: 15.684387141

Break this problem into two subproblems by setting 
(x + 14) equal to 15.684387141 and -15.684387141.

Subproblem 1

x + 14 = 15.684387141 Simplifying x + 14 = 15.684387141 Reorder the terms: 14 + x = 15.684387141 Solving 14 + x = 15.684387141 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 = 15.684387141 + -14 Combine like terms: 14 + -14 = 0 0 + x = 15.684387141 + -14 x = 15.684387141 + -14 Combine like terms: 15.684387141 + -14 = 1.684387141 x = 1.684387141 Simplifying x = 1.684387141

Subproblem 2

x + 14 = -15.684387141 Simplifying x + 14 = -15.684387141 Reorder the terms: 14 + x = -15.684387141 Solving 14 + x = -15.684387141 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 = -15.684387141 + -14 Combine like terms: 14 + -14 = 0 0 + x = -15.684387141 + -14 x = -15.684387141 + -14 Combine like terms: -15.684387141 + -14 = -29.684387141 x = -29.684387141 Simplifying x = -29.684387141

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.684387141, -29.684387141}

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