20x^2-15-3x=0

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Solution for 20x^2-15-3x=0 equation:


Simplifying
20x2 + -15 + -3x = 0

Reorder the terms:
-15 + -3x + 20x2 = 0

Solving
-15 + -3x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-0.75 + -0.15x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -0.15x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -0.15x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -0.15x + x2 = 0 + 0.75
-0.15x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-0.15x + x2 = 0.75

The x term is -0.15x.  Take half its coefficient (-0.075).
Square it (0.005625) and add it to both sides.

Add '0.005625' to each side of the equation.
-0.15x + 0.005625 + x2 = 0.75 + 0.005625

Reorder the terms:
0.005625 + -0.15x + x2 = 0.75 + 0.005625

Combine like terms: 0.75 + 0.005625 = 0.755625
0.005625 + -0.15x + x2 = 0.755625

Factor a perfect square on the left side:
(x + -0.075)(x + -0.075) = 0.755625

Calculate the square root of the right side: 0.869266933

Break this problem into two subproblems by setting 
(x + -0.075) equal to 0.869266933 and -0.869266933.

Subproblem 1

x + -0.075 = 0.869266933 Simplifying x + -0.075 = 0.869266933 Reorder the terms: -0.075 + x = 0.869266933 Solving -0.075 + x = 0.869266933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = 0.869266933 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = 0.869266933 + 0.075 x = 0.869266933 + 0.075 Combine like terms: 0.869266933 + 0.075 = 0.944266933 x = 0.944266933 Simplifying x = 0.944266933

Subproblem 2

x + -0.075 = -0.869266933 Simplifying x + -0.075 = -0.869266933 Reorder the terms: -0.075 + x = -0.869266933 Solving -0.075 + x = -0.869266933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = -0.869266933 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = -0.869266933 + 0.075 x = -0.869266933 + 0.075 Combine like terms: -0.869266933 + 0.075 = -0.794266933 x = -0.794266933 Simplifying x = -0.794266933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.944266933, -0.794266933}

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