-10x^2+140x+0=-3x^2+30x+72

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Solution for -10x^2+140x+0=-3x^2+30x+72 equation: 


Simplifying
-10x2 + 140x + 0 = -3x2 + 30x + 72

Reorder the terms:
0 + 140x + -10x2 = -3x2 + 30x + 72
Remove the zero:
140x + -10x2 = -3x2 + 30x + 72

Reorder the terms:
140x + -10x2 = 72 + 30x + -3x2

Solving
140x + -10x2 = 72 + 30x + -3x2

Solving for variable 'x'.

Reorder the terms:
-72 + 140x + -30x + -10x2 + 3x2 = 72 + 30x + -3x2 + -72 + -30x + 3x2

Combine like terms: 140x + -30x = 110x
-72 + 110x + -10x2 + 3x2 = 72 + 30x + -3x2 + -72 + -30x + 3x2

Combine like terms: -10x2 + 3x2 = -7x2
-72 + 110x + -7x2 = 72 + 30x + -3x2 + -72 + -30x + 3x2

Reorder the terms:
-72 + 110x + -7x2 = 72 + -72 + 30x + -30x + -3x2 + 3x2

Combine like terms: 72 + -72 = 0
-72 + 110x + -7x2 = 0 + 30x + -30x + -3x2 + 3x2
-72 + 110x + -7x2 = 30x + -30x + -3x2 + 3x2

Combine like terms: 30x + -30x = 0
-72 + 110x + -7x2 = 0 + -3x2 + 3x2
-72 + 110x + -7x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-72 + 110x + -7x2 = 0

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

Divide each side by '-7'.
10.28571429 + -15.71428571x + x2 = 0

Move the constant term to the right:

Add '-10.28571429' to each side of the equation.
10.28571429 + -15.71428571x + -10.28571429 + x2 = 0 + -10.28571429

Reorder the terms:
10.28571429 + -10.28571429 + -15.71428571x + x2 = 0 + -10.28571429

Combine like terms: 10.28571429 + -10.28571429 = 0.00000000
0.00000000 + -15.71428571x + x2 = 0 + -10.28571429
-15.71428571x + x2 = 0 + -10.28571429

Combine like terms: 0 + -10.28571429 = -10.28571429
-15.71428571x + x2 = -10.28571429

The x term is -15.71428571x.  Take half its coefficient (-7.857142855).
Square it (61.73469384) and add it to both sides.

Add '61.73469384' to each side of the equation.
-15.71428571x + 61.73469384 + x2 = -10.28571429 + 61.73469384

Reorder the terms:
61.73469384 + -15.71428571x + x2 = -10.28571429 + 61.73469384

Combine like terms: -10.28571429 + 61.73469384 = 51.44897955
61.73469384 + -15.71428571x + x2 = 51.44897955

Factor a perfect square on the left side:
(x + -7.857142855)(x + -7.857142855) = 51.44897955

Calculate the square root of the right side: 7.172794403

Break this problem into two subproblems by setting 
(x + -7.857142855) equal to 7.172794403 and -7.172794403.


Subproblem 1
x + -7.857142855 = 7.172794403

Simplifying
x + -7.857142855 = 7.172794403

Reorder the terms:
-7.857142855 + x = 7.172794403

Solving
-7.857142855 + x = 7.172794403

Solving for variable 'x'.

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

Add '7.857142855' to each side of the equation.
-7.857142855 + 7.857142855 + x = 7.172794403 + 7.857142855

Combine like terms: -7.857142855 + 7.857142855 = 0.000000000
0.000000000 + x = 7.172794403 + 7.857142855
x = 7.172794403 + 7.857142855

Combine like terms: 7.172794403 + 7.857142855 = 15.029937258
x = 15.029937258

Simplifying
x = 15.029937258


Subproblem 2
x + -7.857142855 = -7.172794403

Simplifying
x + -7.857142855 = -7.172794403

Reorder the terms:
-7.857142855 + x = -7.172794403

Solving
-7.857142855 + x = -7.172794403

Solving for variable 'x'.

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

Add '7.857142855' to each side of the equation.
-7.857142855 + 7.857142855 + x = -7.172794403 + 7.857142855

Combine like terms: -7.857142855 + 7.857142855 = 0.000000000
0.000000000 + x = -7.172794403 + 7.857142855
x = -7.172794403 + 7.857142855

Combine like terms: -7.172794403 + 7.857142855 = 0.684348452
x = 0.684348452

Simplifying
x = 0.684348452


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.029937258, 0.684348452}

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