X^2+X-783=0

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Solution for X^2+X-783=0 equation:


Simplifying
X2 + X + -783 = 0

Reorder the terms:
-783 + X + X2 = 0

Solving
-783 + X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '783' to each side of the equation.
-783 + X + 783 + X2 = 0 + 783

Reorder the terms:
-783 + 783 + X + X2 = 0 + 783

Combine like terms: -783 + 783 = 0
0 + X + X2 = 0 + 783
X + X2 = 0 + 783

Combine like terms: 0 + 783 = 783
X + X2 = 783

The X term is X.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
X + 0.25 + X2 = 783 + 0.25

Reorder the terms:
0.25 + X + X2 = 783 + 0.25

Combine like terms: 783 + 0.25 = 783.25
0.25 + X + X2 = 783.25

Factor a perfect square on the left side:
(X + 0.5)(X + 0.5) = 783.25

Calculate the square root of the right side: 27.986603938

Break this problem into two subproblems by setting 
(X + 0.5) equal to 27.986603938 and -27.986603938.

Subproblem 1

X + 0.5 = 27.986603938 Simplifying X + 0.5 = 27.986603938 Reorder the terms: 0.5 + X = 27.986603938 Solving 0.5 + X = 27.986603938 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 27.986603938 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 27.986603938 + -0.5 X = 27.986603938 + -0.5 Combine like terms: 27.986603938 + -0.5 = 27.486603938 X = 27.486603938 Simplifying X = 27.486603938

Subproblem 2

X + 0.5 = -27.986603938 Simplifying X + 0.5 = -27.986603938 Reorder the terms: 0.5 + X = -27.986603938 Solving 0.5 + X = -27.986603938 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -27.986603938 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -27.986603938 + -0.5 X = -27.986603938 + -0.5 Combine like terms: -27.986603938 + -0.5 = -28.486603938 X = -28.486603938 Simplifying X = -28.486603938

Solution

The solution to the problem is based on the solutions from the subproblems. X = {27.486603938, -28.486603938}

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