7x^2+39x-90=0

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Solution for 7x^2+39x-90=0 equation:


Simplifying
7x2 + 39x + -90 = 0

Reorder the terms:
-90 + 39x + 7x2 = 0

Solving
-90 + 39x + 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'.
-12.85714286 + 5.571428571x + x2 = 0

Move the constant term to the right:

Add '12.85714286' to each side of the equation.
-12.85714286 + 5.571428571x + 12.85714286 + x2 = 0 + 12.85714286

Reorder the terms:
-12.85714286 + 12.85714286 + 5.571428571x + x2 = 0 + 12.85714286

Combine like terms: -12.85714286 + 12.85714286 = 0.00000000
0.00000000 + 5.571428571x + x2 = 0 + 12.85714286
5.571428571x + x2 = 0 + 12.85714286

Combine like terms: 0 + 12.85714286 = 12.85714286
5.571428571x + x2 = 12.85714286

The x term is 5.571428571x.  Take half its coefficient (2.785714286).
Square it (7.760204083) and add it to both sides.

Add '7.760204083' to each side of the equation.
5.571428571x + 7.760204083 + x2 = 12.85714286 + 7.760204083

Reorder the terms:
7.760204083 + 5.571428571x + x2 = 12.85714286 + 7.760204083

Combine like terms: 12.85714286 + 7.760204083 = 20.617346943
7.760204083 + 5.571428571x + x2 = 20.617346943

Factor a perfect square on the left side:
(x + 2.785714286)(x + 2.785714286) = 20.617346943

Calculate the square root of the right side: 4.540632879

Break this problem into two subproblems by setting 
(x + 2.785714286) equal to 4.540632879 and -4.540632879.

Subproblem 1

x + 2.785714286 = 4.540632879 Simplifying x + 2.785714286 = 4.540632879 Reorder the terms: 2.785714286 + x = 4.540632879 Solving 2.785714286 + x = 4.540632879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.785714286' to each side of the equation. 2.785714286 + -2.785714286 + x = 4.540632879 + -2.785714286 Combine like terms: 2.785714286 + -2.785714286 = 0.000000000 0.000000000 + x = 4.540632879 + -2.785714286 x = 4.540632879 + -2.785714286 Combine like terms: 4.540632879 + -2.785714286 = 1.754918593 x = 1.754918593 Simplifying x = 1.754918593

Subproblem 2

x + 2.785714286 = -4.540632879 Simplifying x + 2.785714286 = -4.540632879 Reorder the terms: 2.785714286 + x = -4.540632879 Solving 2.785714286 + x = -4.540632879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.785714286' to each side of the equation. 2.785714286 + -2.785714286 + x = -4.540632879 + -2.785714286 Combine like terms: 2.785714286 + -2.785714286 = 0.000000000 0.000000000 + x = -4.540632879 + -2.785714286 x = -4.540632879 + -2.785714286 Combine like terms: -4.540632879 + -2.785714286 = -7.326347165 x = -7.326347165 Simplifying x = -7.326347165

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.754918593, -7.326347165}

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