-15x^2+98x-140=0

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Solution for -15x^2+98x-140=0 equation: 


Simplifying
-15x2 + 98x + -140 = 0

Reorder the terms:
-140 + 98x + -15x2 = 0

Solving
-140 + 98x + -15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
9.333333333 + -6.533333333x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + -6.533333333x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + -6.533333333x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + -6.533333333x + x2 = 0 + -9.333333333
-6.533333333x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
-6.533333333x + x2 = -9.333333333

The x term is -6.533333333x.  Take half its coefficient (-3.266666667).
Square it (10.67111111) and add it to both sides.

Add '10.67111111' to each side of the equation.
-6.533333333x + 10.67111111 + x2 = -9.333333333 + 10.67111111

Reorder the terms:
10.67111111 + -6.533333333x + x2 = -9.333333333 + 10.67111111

Combine like terms: -9.333333333 + 10.67111111 = 1.337777777
10.67111111 + -6.533333333x + x2 = 1.337777777

Factor a perfect square on the left side:
(x + -3.266666667)(x + -3.266666667) = 1.337777777

Calculate the square root of the right side: 1.156623438

Break this problem into two subproblems by setting 
(x + -3.266666667) equal to 1.156623438 and -1.156623438.


Subproblem 1
x + -3.266666667 = 1.156623438

Simplifying
x + -3.266666667 = 1.156623438

Reorder the terms:
-3.266666667 + x = 1.156623438

Solving
-3.266666667 + x = 1.156623438

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.266666667' to each side of the equation.
-3.266666667 + 3.266666667 + x = 1.156623438 + 3.266666667

Combine like terms: -3.266666667 + 3.266666667 = 0.000000000
0.000000000 + x = 1.156623438 + 3.266666667
x = 1.156623438 + 3.266666667

Combine like terms: 1.156623438 + 3.266666667 = 4.423290105
x = 4.423290105

Simplifying
x = 4.423290105


Subproblem 2
x + -3.266666667 = -1.156623438

Simplifying
x + -3.266666667 = -1.156623438

Reorder the terms:
-3.266666667 + x = -1.156623438

Solving
-3.266666667 + x = -1.156623438

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.266666667' to each side of the equation.
-3.266666667 + 3.266666667 + x = -1.156623438 + 3.266666667

Combine like terms: -3.266666667 + 3.266666667 = 0.000000000
0.000000000 + x = -1.156623438 + 3.266666667
x = -1.156623438 + 3.266666667

Combine like terms: -1.156623438 + 3.266666667 = 2.110043229
x = 2.110043229

Simplifying
x = 2.110043229


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.423290105, 2.110043229}

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