2x^2+3x=180

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


Simplifying
2x2 + 3x = 180

Reorder the terms:
3x + 2x2 = 180

Solving
3x + 2x2 = 180

Solving for variable 'x'.

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

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

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

Divide each side by '2'.
-90 + 1.5x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 1.5x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 1.5x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 1.5x + x2 = 0 + 90
1.5x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
1.5x + x2 = 90

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 90 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 90 + 0.5625

Combine like terms: 90 + 0.5625 = 90.5625
0.5625 + 1.5x + x2 = 90.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 90.5625

Calculate the square root of the right side: 9.516433155

Break this problem into two subproblems by setting 
(x + 0.75) equal to 9.516433155 and -9.516433155.

Subproblem 1

x + 0.75 = 9.516433155 Simplifying x + 0.75 = 9.516433155 Reorder the terms: 0.75 + x = 9.516433155 Solving 0.75 + x = 9.516433155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 9.516433155 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 9.516433155 + -0.75 x = 9.516433155 + -0.75 Combine like terms: 9.516433155 + -0.75 = 8.766433155 x = 8.766433155 Simplifying x = 8.766433155

Subproblem 2

x + 0.75 = -9.516433155 Simplifying x + 0.75 = -9.516433155 Reorder the terms: 0.75 + x = -9.516433155 Solving 0.75 + x = -9.516433155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -9.516433155 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -9.516433155 + -0.75 x = -9.516433155 + -0.75 Combine like terms: -9.516433155 + -0.75 = -10.266433155 x = -10.266433155 Simplifying x = -10.266433155

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.766433155, -10.266433155}

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