9x^2+13x-90=0

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Solution for 9x^2+13x-90=0 equation:


Simplifying
9x2 + 13x + -90 = 0

Reorder the terms:
-90 + 13x + 9x2 = 0

Solving
-90 + 13x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-10 + 1.444444444x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 1.444444444x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 1.444444444x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 1.444444444x + x2 = 0 + 10
1.444444444x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
1.444444444x + x2 = 10

The x term is 1.444444444x.  Take half its coefficient (0.722222222).
Square it (0.5216049380) and add it to both sides.

Add '0.5216049380' to each side of the equation.
1.444444444x + 0.5216049380 + x2 = 10 + 0.5216049380

Reorder the terms:
0.5216049380 + 1.444444444x + x2 = 10 + 0.5216049380

Combine like terms: 10 + 0.5216049380 = 10.521604938
0.5216049380 + 1.444444444x + x2 = 10.521604938

Factor a perfect square on the left side:
(x + 0.722222222)(x + 0.722222222) = 10.521604938

Calculate the square root of the right side: 3.24370235

Break this problem into two subproblems by setting 
(x + 0.722222222) equal to 3.24370235 and -3.24370235.

Subproblem 1

x + 0.722222222 = 3.24370235 Simplifying x + 0.722222222 = 3.24370235 Reorder the terms: 0.722222222 + x = 3.24370235 Solving 0.722222222 + x = 3.24370235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = 3.24370235 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = 3.24370235 + -0.722222222 x = 3.24370235 + -0.722222222 Combine like terms: 3.24370235 + -0.722222222 = 2.521480128 x = 2.521480128 Simplifying x = 2.521480128

Subproblem 2

x + 0.722222222 = -3.24370235 Simplifying x + 0.722222222 = -3.24370235 Reorder the terms: 0.722222222 + x = -3.24370235 Solving 0.722222222 + x = -3.24370235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = -3.24370235 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = -3.24370235 + -0.722222222 x = -3.24370235 + -0.722222222 Combine like terms: -3.24370235 + -0.722222222 = -3.965924572 x = -3.965924572 Simplifying x = -3.965924572

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.521480128, -3.965924572}

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