96=3x+1x*x+1

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Solution for 96=3x+1x*x+1 equation:


Simplifying
96 = 3x + 1x * x + 1

Multiply x * x
96 = 3x + 1x2 + 1

Reorder the terms:
96 = 1 + 3x + 1x2

Solving
96 = 1 + 3x + 1x2

Solving for variable 'x'.

Combine like terms: 96 + -1 = 95
95 + -3x + -1x2 = 1 + 3x + 1x2 + -1 + -3x + -1x2

Reorder the terms:
95 + -3x + -1x2 = 1 + -1 + 3x + -3x + 1x2 + -1x2

Combine like terms: 1 + -1 = 0
95 + -3x + -1x2 = 0 + 3x + -3x + 1x2 + -1x2
95 + -3x + -1x2 = 3x + -3x + 1x2 + -1x2

Combine like terms: 3x + -3x = 0
95 + -3x + -1x2 = 0 + 1x2 + -1x2
95 + -3x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
95 + -3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-95 + 3x + x2 = 0

Move the constant term to the right:

Add '95' to each side of the equation.
-95 + 3x + 95 + x2 = 0 + 95

Reorder the terms:
-95 + 95 + 3x + x2 = 0 + 95

Combine like terms: -95 + 95 = 0
0 + 3x + x2 = 0 + 95
3x + x2 = 0 + 95

Combine like terms: 0 + 95 = 95
3x + x2 = 95

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 = 95 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 95 + 2.25

Combine like terms: 95 + 2.25 = 97.25
2.25 + 3x + x2 = 97.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 97.25

Calculate the square root of the right side: 9.861541462

Break this problem into two subproblems by setting 
(x + 1.5) equal to 9.861541462 and -9.861541462.

Subproblem 1

x + 1.5 = 9.861541462 Simplifying x + 1.5 = 9.861541462 Reorder the terms: 1.5 + x = 9.861541462 Solving 1.5 + x = 9.861541462 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 = 9.861541462 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.861541462 + -1.5 x = 9.861541462 + -1.5 Combine like terms: 9.861541462 + -1.5 = 8.361541462 x = 8.361541462 Simplifying x = 8.361541462

Subproblem 2

x + 1.5 = -9.861541462 Simplifying x + 1.5 = -9.861541462 Reorder the terms: 1.5 + x = -9.861541462 Solving 1.5 + x = -9.861541462 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 = -9.861541462 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.861541462 + -1.5 x = -9.861541462 + -1.5 Combine like terms: -9.861541462 + -1.5 = -11.361541462 x = -11.361541462 Simplifying x = -11.361541462

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.361541462, -11.361541462}

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