3X+X^2=74

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Solution for 3X+X^2=74 equation:


Simplifying
3X + X2 = 74

Solving
3X + X2 = 74

Solving for variable 'X'.

Reorder the terms:
-74 + 3X + X2 = 74 + -74

Combine like terms: 74 + -74 = 0
-74 + 3X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + 3X + 74 + X2 = 0 + 74

Reorder the terms:
-74 + 74 + 3X + X2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + 3X + X2 = 0 + 74
3X + X2 = 0 + 74

Combine like terms: 0 + 74 = 74
3X + X2 = 74

The X term is 3X.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3X + 2.25 + X2 = 74 + 2.25

Reorder the terms:
2.25 + 3X + X2 = 74 + 2.25

Combine like terms: 74 + 2.25 = 76.25
2.25 + 3X + X2 = 76.25

Factor a perfect square on the left side:
(X + 1.5)(X + 1.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(X + 1.5) equal to 8.732124598 and -8.732124598.

Subproblem 1

X + 1.5 = 8.732124598 Simplifying X + 1.5 = 8.732124598 Reorder the terms: 1.5 + X = 8.732124598 Solving 1.5 + X = 8.732124598 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = 8.732124598 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 8.732124598 + -1.5 X = 8.732124598 + -1.5 Combine like terms: 8.732124598 + -1.5 = 7.232124598 X = 7.232124598 Simplifying X = 7.232124598

Subproblem 2

X + 1.5 = -8.732124598 Simplifying X + 1.5 = -8.732124598 Reorder the terms: 1.5 + X = -8.732124598 Solving 1.5 + X = -8.732124598 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = -8.732124598 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -8.732124598 + -1.5 X = -8.732124598 + -1.5 Combine like terms: -8.732124598 + -1.5 = -10.232124598 X = -10.232124598 Simplifying X = -10.232124598

Solution

The solution to the problem is based on the solutions from the subproblems. X = {7.232124598, -10.232124598}

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