30x*30x+11x-30=0

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Solution for 30x*30x+11x-30=0 equation:


Simplifying
30x * 30x + 11x + -30 = 0

Reorder the terms for easier multiplication:
30 * 30x * x + 11x + -30 = 0

Multiply 30 * 30
900x * x + 11x + -30 = 0

Multiply x * x
900x2 + 11x + -30 = 0

Reorder the terms:
-30 + 11x + 900x2 = 0

Solving
-30 + 11x + 900x2 = 0

Solving for variable 'x'.

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

Divide each side by '900'.
-0.03333333333 + 0.01222222222x + x2 = 0.00

Move the constant term to the right:

Add '0.03333333333' to each side of the equation.
-0.03333333333 + 0.01222222222x + 0.03333333333 + x2 = 0.00 + 0.03333333333

Reorder the terms:
-0.03333333333 + 0.03333333333 + 0.01222222222x + x2 = 0.00 + 0.03333333333

Combine like terms: -0.03333333333 + 0.03333333333 = 0.00000000000
0.00000000000 + 0.01222222222x + x2 = 0.00 + 0.03333333333
0.01222222222x + x2 = 0.00 + 0.03333333333

Combine like terms: 0.00 + 0.03333333333 = 0.03333333333
0.01222222222x + x2 = 0.03333333333

The x term is 0.01222222222x.  Take half its coefficient (0.00611111111).
Square it (0.00003734567900) and add it to both sides.

Add '0.00003734567900' to each side of the equation.
0.01222222222x + 0.00003734567900 + x2 = 0.03333333333 + 0.00003734567900

Reorder the terms:
0.00003734567900 + 0.01222222222x + x2 = 0.03333333333 + 0.00003734567900

Combine like terms: 0.03333333333 + 0.00003734567900 = 0.033370679009
0.00003734567900 + 0.01222222222x + x2 = 0.033370679009

Factor a perfect square on the left side:
(x + 0.00611111111)(x + 0.00611111111) = 0.033370679009

Calculate the square root of the right side: 0.182676433

Break this problem into two subproblems by setting 
(x + 0.00611111111) equal to 0.182676433 and -0.182676433.

Subproblem 1

x + 0.00611111111 = 0.182676433 Simplifying x + 0.00611111111 = 0.182676433 Reorder the terms: 0.00611111111 + x = 0.182676433 Solving 0.00611111111 + x = 0.182676433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00611111111' to each side of the equation. 0.00611111111 + -0.00611111111 + x = 0.182676433 + -0.00611111111 Combine like terms: 0.00611111111 + -0.00611111111 = 0.00000000000 0.00000000000 + x = 0.182676433 + -0.00611111111 x = 0.182676433 + -0.00611111111 Combine like terms: 0.182676433 + -0.00611111111 = 0.17656532189 x = 0.17656532189 Simplifying x = 0.17656532189

Subproblem 2

x + 0.00611111111 = -0.182676433 Simplifying x + 0.00611111111 = -0.182676433 Reorder the terms: 0.00611111111 + x = -0.182676433 Solving 0.00611111111 + x = -0.182676433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00611111111' to each side of the equation. 0.00611111111 + -0.00611111111 + x = -0.182676433 + -0.00611111111 Combine like terms: 0.00611111111 + -0.00611111111 = 0.00000000000 0.00000000000 + x = -0.182676433 + -0.00611111111 x = -0.182676433 + -0.00611111111 Combine like terms: -0.182676433 + -0.00611111111 = -0.18878754411 x = -0.18878754411 Simplifying x = -0.18878754411

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.17656532189, -0.18878754411}

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