3x^2+2x+45=180

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Solution for 3x^2+2x+45=180 equation:


Simplifying
3x2 + 2x + 45 = 180

Reorder the terms:
45 + 2x + 3x2 = 180

Solving
45 + 2x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
45 + -180 + 2x + 3x2 = 180 + -180

Combine like terms: 45 + -180 = -135
-135 + 2x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-135 + 2x + 3x2 = 0

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

Divide each side by '3'.
-45 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 0.6666666667x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 0.6666666667x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 0.6666666667x + x2 = 0 + 45
0.6666666667x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
0.6666666667x + x2 = 45

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 45 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 45 + 0.1111111112

Combine like terms: 45 + 0.1111111112 = 45.1111111112
0.1111111112 + 0.6666666667x + x2 = 45.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 45.1111111112

Calculate the square root of the right side: 6.71648056

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 6.71648056 and -6.71648056.

Subproblem 1

x + 0.3333333334 = 6.71648056 Simplifying x + 0.3333333334 = 6.71648056 Reorder the terms: 0.3333333334 + x = 6.71648056 Solving 0.3333333334 + x = 6.71648056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 6.71648056 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 6.71648056 + -0.3333333334 x = 6.71648056 + -0.3333333334 Combine like terms: 6.71648056 + -0.3333333334 = 6.3831472266 x = 6.3831472266 Simplifying x = 6.3831472266

Subproblem 2

x + 0.3333333334 = -6.71648056 Simplifying x + 0.3333333334 = -6.71648056 Reorder the terms: 0.3333333334 + x = -6.71648056 Solving 0.3333333334 + x = -6.71648056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -6.71648056 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -6.71648056 + -0.3333333334 x = -6.71648056 + -0.3333333334 Combine like terms: -6.71648056 + -0.3333333334 = -7.0498138934 x = -7.0498138934 Simplifying x = -7.0498138934

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.3831472266, -7.0498138934}

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