5x^2+6x=18-3

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Solution for 5x^2+6x=18-3 equation:


Simplifying
5x2 + 6x = 18 + -3

Reorder the terms:
6x + 5x2 = 18 + -3

Combine like terms: 18 + -3 = 15
6x + 5x2 = 15

Solving
6x + 5x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + 6x + 5x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 6x + 5x2 = 0

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

Divide each side by '5'.
-3 + 1.2x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 1.2x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 1.2x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1.2x + x2 = 0 + 3
1.2x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
1.2x + x2 = 3

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = 3 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 3 + 0.36

Combine like terms: 3 + 0.36 = 3.36
0.36 + 1.2x + x2 = 3.36

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 3.36

Calculate the square root of the right side: 1.833030278

Break this problem into two subproblems by setting 
(x + 0.6) equal to 1.833030278 and -1.833030278.

Subproblem 1

x + 0.6 = 1.833030278 Simplifying x + 0.6 = 1.833030278 Reorder the terms: 0.6 + x = 1.833030278 Solving 0.6 + x = 1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 1.833030278 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.833030278 + -0.6 x = 1.833030278 + -0.6 Combine like terms: 1.833030278 + -0.6 = 1.233030278 x = 1.233030278 Simplifying x = 1.233030278

Subproblem 2

x + 0.6 = -1.833030278 Simplifying x + 0.6 = -1.833030278 Reorder the terms: 0.6 + x = -1.833030278 Solving 0.6 + x = -1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -1.833030278 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.833030278 + -0.6 x = -1.833030278 + -0.6 Combine like terms: -1.833030278 + -0.6 = -2.433030278 x = -2.433030278 Simplifying x = -2.433030278

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.233030278, -2.433030278}

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