22x^2+55x-30=0

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Solution for 22x^2+55x-30=0 equation:


Simplifying
22x2 + 55x + -30 = 0

Reorder the terms:
-30 + 55x + 22x2 = 0

Solving
-30 + 55x + 22x2 = 0

Solving for variable 'x'.

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

Divide each side by '22'.
-1.363636364 + 2.5x + x2 = 0

Move the constant term to the right:

Add '1.363636364' to each side of the equation.
-1.363636364 + 2.5x + 1.363636364 + x2 = 0 + 1.363636364

Reorder the terms:
-1.363636364 + 1.363636364 + 2.5x + x2 = 0 + 1.363636364

Combine like terms: -1.363636364 + 1.363636364 = 0.000000000
0.000000000 + 2.5x + x2 = 0 + 1.363636364
2.5x + x2 = 0 + 1.363636364

Combine like terms: 0 + 1.363636364 = 1.363636364
2.5x + x2 = 1.363636364

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 1.363636364 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 1.363636364 + 1.5625

Combine like terms: 1.363636364 + 1.5625 = 2.926136364
1.5625 + 2.5x + x2 = 2.926136364

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 2.926136364

Calculate the square root of the right side: 1.710595324

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.710595324 and -1.710595324.

Subproblem 1

x + 1.25 = 1.710595324 Simplifying x + 1.25 = 1.710595324 Reorder the terms: 1.25 + x = 1.710595324 Solving 1.25 + x = 1.710595324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.710595324 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.710595324 + -1.25 x = 1.710595324 + -1.25 Combine like terms: 1.710595324 + -1.25 = 0.460595324 x = 0.460595324 Simplifying x = 0.460595324

Subproblem 2

x + 1.25 = -1.710595324 Simplifying x + 1.25 = -1.710595324 Reorder the terms: 1.25 + x = -1.710595324 Solving 1.25 + x = -1.710595324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.710595324 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.710595324 + -1.25 x = -1.710595324 + -1.25 Combine like terms: -1.710595324 + -1.25 = -2.960595324 x = -2.960595324 Simplifying x = -2.960595324

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.460595324, -2.960595324}

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