x^2+4x-78=0

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Solution for x^2+4x-78=0 equation:


Simplifying
x2 + 4x + -78 = 0

Reorder the terms:
-78 + 4x + x2 = 0

Solving
-78 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + 4x + 78 + x2 = 0 + 78

Reorder the terms:
-78 + 78 + 4x + x2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + 4x + x2 = 0 + 78
4x + x2 = 0 + 78

Combine like terms: 0 + 78 = 78
4x + x2 = 78

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 78 + 4

Reorder the terms:
4 + 4x + x2 = 78 + 4

Combine like terms: 78 + 4 = 82
4 + 4x + x2 = 82

Factor a perfect square on the left side:
(x + 2)(x + 2) = 82

Calculate the square root of the right side: 9.055385138

Break this problem into two subproblems by setting 
(x + 2) equal to 9.055385138 and -9.055385138.

Subproblem 1

x + 2 = 9.055385138 Simplifying x + 2 = 9.055385138 Reorder the terms: 2 + x = 9.055385138 Solving 2 + x = 9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.055385138 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.055385138 + -2 x = 9.055385138 + -2 Combine like terms: 9.055385138 + -2 = 7.055385138 x = 7.055385138 Simplifying x = 7.055385138

Subproblem 2

x + 2 = -9.055385138 Simplifying x + 2 = -9.055385138 Reorder the terms: 2 + x = -9.055385138 Solving 2 + x = -9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.055385138 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.055385138 + -2 x = -9.055385138 + -2 Combine like terms: -9.055385138 + -2 = -11.055385138 x = -11.055385138 Simplifying x = -11.055385138

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.055385138, -11.055385138}

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