45x^2+2x-30=0

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Solution for 45x^2+2x-30=0 equation:


Simplifying
45x2 + 2x + -30 = 0

Reorder the terms:
-30 + 2x + 45x2 = 0

Solving
-30 + 2x + 45x2 = 0

Solving for variable 'x'.

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

Divide each side by '45'.
-0.6666666667 + 0.04444444444x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 0.04444444444x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 0.04444444444x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 0.04444444444x + x2 = 0 + 0.6666666667
0.04444444444x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
0.04444444444x + x2 = 0.6666666667

The x term is 0.04444444444x.  Take half its coefficient (0.02222222222).
Square it (0.0004938271604) and add it to both sides.

Add '0.0004938271604' to each side of the equation.
0.04444444444x + 0.0004938271604 + x2 = 0.6666666667 + 0.0004938271604

Reorder the terms:
0.0004938271604 + 0.04444444444x + x2 = 0.6666666667 + 0.0004938271604

Combine like terms: 0.6666666667 + 0.0004938271604 = 0.6671604938604
0.0004938271604 + 0.04444444444x + x2 = 0.6671604938604

Factor a perfect square on the left side:
(x + 0.02222222222)(x + 0.02222222222) = 0.6671604938604

Calculate the square root of the right side: 0.816798931

Break this problem into two subproblems by setting 
(x + 0.02222222222) equal to 0.816798931 and -0.816798931.

Subproblem 1

x + 0.02222222222 = 0.816798931 Simplifying x + 0.02222222222 = 0.816798931 Reorder the terms: 0.02222222222 + x = 0.816798931 Solving 0.02222222222 + x = 0.816798931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02222222222' to each side of the equation. 0.02222222222 + -0.02222222222 + x = 0.816798931 + -0.02222222222 Combine like terms: 0.02222222222 + -0.02222222222 = 0.00000000000 0.00000000000 + x = 0.816798931 + -0.02222222222 x = 0.816798931 + -0.02222222222 Combine like terms: 0.816798931 + -0.02222222222 = 0.79457670878 x = 0.79457670878 Simplifying x = 0.79457670878

Subproblem 2

x + 0.02222222222 = -0.816798931 Simplifying x + 0.02222222222 = -0.816798931 Reorder the terms: 0.02222222222 + x = -0.816798931 Solving 0.02222222222 + x = -0.816798931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02222222222' to each side of the equation. 0.02222222222 + -0.02222222222 + x = -0.816798931 + -0.02222222222 Combine like terms: 0.02222222222 + -0.02222222222 = 0.00000000000 0.00000000000 + x = -0.816798931 + -0.02222222222 x = -0.816798931 + -0.02222222222 Combine like terms: -0.816798931 + -0.02222222222 = -0.83902115322 x = -0.83902115322 Simplifying x = -0.83902115322

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.79457670878, -0.83902115322}

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