30x^2+44x-7=

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Solution for 30x^2+44x-7= equation:


Simplifying
30x2 + 44x + -7 = 0

Reorder the terms:
-7 + 44x + 30x2 = 0

Solving
-7 + 44x + 30x2 = 0

Solving for variable 'x'.

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

Divide each side by '30'.
-0.2333333333 + 1.466666667x + x2 = 0

Move the constant term to the right:

Add '0.2333333333' to each side of the equation.
-0.2333333333 + 1.466666667x + 0.2333333333 + x2 = 0 + 0.2333333333

Reorder the terms:
-0.2333333333 + 0.2333333333 + 1.466666667x + x2 = 0 + 0.2333333333

Combine like terms: -0.2333333333 + 0.2333333333 = 0.0000000000
0.0000000000 + 1.466666667x + x2 = 0 + 0.2333333333
1.466666667x + x2 = 0 + 0.2333333333

Combine like terms: 0 + 0.2333333333 = 0.2333333333
1.466666667x + x2 = 0.2333333333

The x term is 1.466666667x.  Take half its coefficient (0.7333333335).
Square it (0.5377777780) and add it to both sides.

Add '0.5377777780' to each side of the equation.
1.466666667x + 0.5377777780 + x2 = 0.2333333333 + 0.5377777780

Reorder the terms:
0.5377777780 + 1.466666667x + x2 = 0.2333333333 + 0.5377777780

Combine like terms: 0.2333333333 + 0.5377777780 = 0.7711111113
0.5377777780 + 1.466666667x + x2 = 0.7711111113

Factor a perfect square on the left side:
(x + 0.7333333335)(x + 0.7333333335) = 0.7711111113

Calculate the square root of the right side: 0.878129325

Break this problem into two subproblems by setting 
(x + 0.7333333335) equal to 0.878129325 and -0.878129325.

Subproblem 1

x + 0.7333333335 = 0.878129325 Simplifying x + 0.7333333335 = 0.878129325 Reorder the terms: 0.7333333335 + x = 0.878129325 Solving 0.7333333335 + x = 0.878129325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7333333335' to each side of the equation. 0.7333333335 + -0.7333333335 + x = 0.878129325 + -0.7333333335 Combine like terms: 0.7333333335 + -0.7333333335 = 0.0000000000 0.0000000000 + x = 0.878129325 + -0.7333333335 x = 0.878129325 + -0.7333333335 Combine like terms: 0.878129325 + -0.7333333335 = 0.1447959915 x = 0.1447959915 Simplifying x = 0.1447959915

Subproblem 2

x + 0.7333333335 = -0.878129325 Simplifying x + 0.7333333335 = -0.878129325 Reorder the terms: 0.7333333335 + x = -0.878129325 Solving 0.7333333335 + x = -0.878129325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7333333335' to each side of the equation. 0.7333333335 + -0.7333333335 + x = -0.878129325 + -0.7333333335 Combine like terms: 0.7333333335 + -0.7333333335 = 0.0000000000 0.0000000000 + x = -0.878129325 + -0.7333333335 x = -0.878129325 + -0.7333333335 Combine like terms: -0.878129325 + -0.7333333335 = -1.6114626585 x = -1.6114626585 Simplifying x = -1.6114626585

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1447959915, -1.6114626585}

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