2x^2+3x=186

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Solution for 2x^2+3x=186 equation:


Simplifying
2x2 + 3x = 186

Reorder the terms:
3x + 2x2 = 186

Solving
3x + 2x2 = 186

Solving for variable 'x'.

Reorder the terms:
-186 + 3x + 2x2 = 186 + -186

Combine like terms: 186 + -186 = 0
-186 + 3x + 2x2 = 0

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

Divide each side by '2'.
-93 + 1.5x + x2 = 0

Move the constant term to the right:

Add '93' to each side of the equation.
-93 + 1.5x + 93 + x2 = 0 + 93

Reorder the terms:
-93 + 93 + 1.5x + x2 = 0 + 93

Combine like terms: -93 + 93 = 0
0 + 1.5x + x2 = 0 + 93
1.5x + x2 = 0 + 93

Combine like terms: 0 + 93 = 93
1.5x + x2 = 93

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 = 93 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 93 + 0.5625

Combine like terms: 93 + 0.5625 = 93.5625
0.5625 + 1.5x + x2 = 93.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 93.5625

Calculate the square root of the right side: 9.672771061

Break this problem into two subproblems by setting 
(x + 0.75) equal to 9.672771061 and -9.672771061.

Subproblem 1

x + 0.75 = 9.672771061 Simplifying x + 0.75 = 9.672771061 Reorder the terms: 0.75 + x = 9.672771061 Solving 0.75 + x = 9.672771061 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 = 9.672771061 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 9.672771061 + -0.75 x = 9.672771061 + -0.75 Combine like terms: 9.672771061 + -0.75 = 8.922771061 x = 8.922771061 Simplifying x = 8.922771061

Subproblem 2

x + 0.75 = -9.672771061 Simplifying x + 0.75 = -9.672771061 Reorder the terms: 0.75 + x = -9.672771061 Solving 0.75 + x = -9.672771061 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 = -9.672771061 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -9.672771061 + -0.75 x = -9.672771061 + -0.75 Combine like terms: -9.672771061 + -0.75 = -10.422771061 x = -10.422771061 Simplifying x = -10.422771061

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.922771061, -10.422771061}

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