(X^2+X-10)=425

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Solution for (X^2+X-10)=425 equation:


Simplifying
(X2 + X + -10) = 425

Reorder the terms:
(-10 + X + X2) = 425

Remove parenthesis around (-10 + X + X2)
-10 + X + X2 = 425

Solving
-10 + X + X2 = 425

Solving for variable 'X'.

Reorder the terms:
-10 + -425 + X + X2 = 425 + -425

Combine like terms: -10 + -425 = -435
-435 + X + X2 = 425 + -425

Combine like terms: 425 + -425 = 0
-435 + X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '435' to each side of the equation.
-435 + X + 435 + X2 = 0 + 435

Reorder the terms:
-435 + 435 + X + X2 = 0 + 435

Combine like terms: -435 + 435 = 0
0 + X + X2 = 0 + 435
X + X2 = 0 + 435

Combine like terms: 0 + 435 = 435
X + X2 = 435

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 = 435 + 0.25

Reorder the terms:
0.25 + X + X2 = 435 + 0.25

Combine like terms: 435 + 0.25 = 435.25
0.25 + X + X2 = 435.25

Factor a perfect square on the left side:
(X + 0.5)(X + 0.5) = 435.25

Calculate the square root of the right side: 20.862646045

Break this problem into two subproblems by setting 
(X + 0.5) equal to 20.862646045 and -20.862646045.

Subproblem 1

X + 0.5 = 20.862646045 Simplifying X + 0.5 = 20.862646045 Reorder the terms: 0.5 + X = 20.862646045 Solving 0.5 + X = 20.862646045 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 = 20.862646045 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 20.862646045 + -0.5 X = 20.862646045 + -0.5 Combine like terms: 20.862646045 + -0.5 = 20.362646045 X = 20.362646045 Simplifying X = 20.362646045

Subproblem 2

X + 0.5 = -20.862646045 Simplifying X + 0.5 = -20.862646045 Reorder the terms: 0.5 + X = -20.862646045 Solving 0.5 + X = -20.862646045 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 = -20.862646045 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -20.862646045 + -0.5 X = -20.862646045 + -0.5 Combine like terms: -20.862646045 + -0.5 = -21.362646045 X = -21.362646045 Simplifying X = -21.362646045

Solution

The solution to the problem is based on the solutions from the subproblems. X = {20.362646045, -21.362646045}

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