X*X+3X-48=3498

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Solution for X*X+3X-48=3498 equation:


Simplifying
X * X + 3X + -48 = 3498

Multiply X * X
X2 + 3X + -48 = 3498

Reorder the terms:
-48 + 3X + X2 = 3498

Solving
-48 + 3X + X2 = 3498

Solving for variable 'X'.

Reorder the terms:
-48 + -3498 + 3X + X2 = 3498 + -3498

Combine like terms: -48 + -3498 = -3546
-3546 + 3X + X2 = 3498 + -3498

Combine like terms: 3498 + -3498 = 0
-3546 + 3X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3546' to each side of the equation.
-3546 + 3X + 3546 + X2 = 0 + 3546

Reorder the terms:
-3546 + 3546 + 3X + X2 = 0 + 3546

Combine like terms: -3546 + 3546 = 0
0 + 3X + X2 = 0 + 3546
3X + X2 = 0 + 3546

Combine like terms: 0 + 3546 = 3546
3X + X2 = 3546

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 = 3546 + 2.25

Reorder the terms:
2.25 + 3X + X2 = 3546 + 2.25

Combine like terms: 3546 + 2.25 = 3548.25
2.25 + 3X + X2 = 3548.25

Factor a perfect square on the left side:
(X + 1.5)(X + 1.5) = 3548.25

Calculate the square root of the right side: 59.567188955

Break this problem into two subproblems by setting 
(X + 1.5) equal to 59.567188955 and -59.567188955.

Subproblem 1

X + 1.5 = 59.567188955 Simplifying X + 1.5 = 59.567188955 Reorder the terms: 1.5 + X = 59.567188955 Solving 1.5 + X = 59.567188955 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 = 59.567188955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 59.567188955 + -1.5 X = 59.567188955 + -1.5 Combine like terms: 59.567188955 + -1.5 = 58.067188955 X = 58.067188955 Simplifying X = 58.067188955

Subproblem 2

X + 1.5 = -59.567188955 Simplifying X + 1.5 = -59.567188955 Reorder the terms: 1.5 + X = -59.567188955 Solving 1.5 + X = -59.567188955 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 = -59.567188955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -59.567188955 + -1.5 X = -59.567188955 + -1.5 Combine like terms: -59.567188955 + -1.5 = -61.067188955 X = -61.067188955 Simplifying X = -61.067188955

Solution

The solution to the problem is based on the solutions from the subproblems. X = {58.067188955, -61.067188955}

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