7x^2+22x-30=0

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Solution for 7x^2+22x-30=0 equation:


Simplifying
7x2 + 22x + -30 = 0

Reorder the terms:
-30 + 22x + 7x2 = 0

Solving
-30 + 22x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-4.285714286 + 3.142857143x + x2 = 0

Move the constant term to the right:

Add '4.285714286' to each side of the equation.
-4.285714286 + 3.142857143x + 4.285714286 + x2 = 0 + 4.285714286

Reorder the terms:
-4.285714286 + 4.285714286 + 3.142857143x + x2 = 0 + 4.285714286

Combine like terms: -4.285714286 + 4.285714286 = 0.000000000
0.000000000 + 3.142857143x + x2 = 0 + 4.285714286
3.142857143x + x2 = 0 + 4.285714286

Combine like terms: 0 + 4.285714286 = 4.285714286
3.142857143x + x2 = 4.285714286

The x term is 3.142857143x.  Take half its coefficient (1.571428572).
Square it (2.469387757) and add it to both sides.

Add '2.469387757' to each side of the equation.
3.142857143x + 2.469387757 + x2 = 4.285714286 + 2.469387757

Reorder the terms:
2.469387757 + 3.142857143x + x2 = 4.285714286 + 2.469387757

Combine like terms: 4.285714286 + 2.469387757 = 6.755102043
2.469387757 + 3.142857143x + x2 = 6.755102043

Factor a perfect square on the left side:
(x + 1.571428572)(x + 1.571428572) = 6.755102043

Calculate the square root of the right side: 2.599057915

Break this problem into two subproblems by setting 
(x + 1.571428572) equal to 2.599057915 and -2.599057915.

Subproblem 1

x + 1.571428572 = 2.599057915 Simplifying x + 1.571428572 = 2.599057915 Reorder the terms: 1.571428572 + x = 2.599057915 Solving 1.571428572 + x = 2.599057915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = 2.599057915 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = 2.599057915 + -1.571428572 x = 2.599057915 + -1.571428572 Combine like terms: 2.599057915 + -1.571428572 = 1.027629343 x = 1.027629343 Simplifying x = 1.027629343

Subproblem 2

x + 1.571428572 = -2.599057915 Simplifying x + 1.571428572 = -2.599057915 Reorder the terms: 1.571428572 + x = -2.599057915 Solving 1.571428572 + x = -2.599057915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = -2.599057915 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = -2.599057915 + -1.571428572 x = -2.599057915 + -1.571428572 Combine like terms: -2.599057915 + -1.571428572 = -4.170486487 x = -4.170486487 Simplifying x = -4.170486487

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.027629343, -4.170486487}

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