20x^2+7x-6-9=0

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Solution for 20x^2+7x-6-9=0 equation:


Simplifying
20x2 + 7x + -6 + -9 = 0

Reorder the terms:
-6 + -9 + 7x + 20x2 = 0

Combine like terms: -6 + -9 = -15
-15 + 7x + 20x2 = 0

Solving
-15 + 7x + 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 + 0.35x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 0.35x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 0.35x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 0.35x + x2 = 0 + 0.75
0.35x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
0.35x + x2 = 0.75

The x term is 0.35x.  Take half its coefficient (0.175).
Square it (0.030625) and add it to both sides.

Add '0.030625' to each side of the equation.
0.35x + 0.030625 + x2 = 0.75 + 0.030625

Reorder the terms:
0.030625 + 0.35x + x2 = 0.75 + 0.030625

Combine like terms: 0.75 + 0.030625 = 0.780625
0.030625 + 0.35x + x2 = 0.780625

Factor a perfect square on the left side:
(x + 0.175)(x + 0.175) = 0.780625

Calculate the square root of the right side: 0.883529852

Break this problem into two subproblems by setting 
(x + 0.175) equal to 0.883529852 and -0.883529852.

Subproblem 1

x + 0.175 = 0.883529852 Simplifying x + 0.175 = 0.883529852 Reorder the terms: 0.175 + x = 0.883529852 Solving 0.175 + x = 0.883529852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = 0.883529852 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = 0.883529852 + -0.175 x = 0.883529852 + -0.175 Combine like terms: 0.883529852 + -0.175 = 0.708529852 x = 0.708529852 Simplifying x = 0.708529852

Subproblem 2

x + 0.175 = -0.883529852 Simplifying x + 0.175 = -0.883529852 Reorder the terms: 0.175 + x = -0.883529852 Solving 0.175 + x = -0.883529852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = -0.883529852 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = -0.883529852 + -0.175 x = -0.883529852 + -0.175 Combine like terms: -0.883529852 + -0.175 = -1.058529852 x = -1.058529852 Simplifying x = -1.058529852

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.708529852, -1.058529852}

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