x^2+x-97=0

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Solution for x^2+x-97=0 equation:


Simplifying
x2 + x + -97 = 0

Reorder the terms:
-97 + x + x2 = 0

Solving
-97 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '97' to each side of the equation.
-97 + x + 97 + x2 = 0 + 97

Reorder the terms:
-97 + 97 + x + x2 = 0 + 97

Combine like terms: -97 + 97 = 0
0 + x + x2 = 0 + 97
x + x2 = 0 + 97

Combine like terms: 0 + 97 = 97
x + x2 = 97

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 = 97 + 0.25

Reorder the terms:
0.25 + x + x2 = 97 + 0.25

Combine like terms: 97 + 0.25 = 97.25
0.25 + x + x2 = 97.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 97.25

Calculate the square root of the right side: 9.861541462

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.861541462 and -9.861541462.

Subproblem 1

x + 0.5 = 9.861541462 Simplifying x + 0.5 = 9.861541462 Reorder the terms: 0.5 + x = 9.861541462 Solving 0.5 + x = 9.861541462 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 = 9.861541462 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.861541462 + -0.5 x = 9.861541462 + -0.5 Combine like terms: 9.861541462 + -0.5 = 9.361541462 x = 9.361541462 Simplifying x = 9.361541462

Subproblem 2

x + 0.5 = -9.861541462 Simplifying x + 0.5 = -9.861541462 Reorder the terms: 0.5 + x = -9.861541462 Solving 0.5 + x = -9.861541462 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 = -9.861541462 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.861541462 + -0.5 x = -9.861541462 + -0.5 Combine like terms: -9.861541462 + -0.5 = -10.361541462 x = -10.361541462 Simplifying x = -10.361541462

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.361541462, -10.361541462}

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