5x^2-10x+7-4x-14x^2=

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Solution for 5x^2-10x+7-4x-14x^2= equation:


Simplifying
5x2 + -10x + 7 + -4x + -14x2 = 0

Reorder the terms:
7 + -10x + -4x + 5x2 + -14x2 = 0

Combine like terms: -10x + -4x = -14x
7 + -14x + 5x2 + -14x2 = 0

Combine like terms: 5x2 + -14x2 = -9x2
7 + -14x + -9x2 = 0

Solving
7 + -14x + -9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.7777777778 + 1.555555556x + x2 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + 1.555555556x + 0.7777777778 + x2 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + 1.555555556x + x2 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + 1.555555556x + x2 = 0 + 0.7777777778
1.555555556x + x2 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
1.555555556x + x2 = 0.7777777778

The x term is 1.555555556x.  Take half its coefficient (0.777777778).
Square it (0.6049382720) and add it to both sides.

Add '0.6049382720' to each side of the equation.
1.555555556x + 0.6049382720 + x2 = 0.7777777778 + 0.6049382720

Reorder the terms:
0.6049382720 + 1.555555556x + x2 = 0.7777777778 + 0.6049382720

Combine like terms: 0.7777777778 + 0.6049382720 = 1.3827160498
0.6049382720 + 1.555555556x + x2 = 1.3827160498

Factor a perfect square on the left side:
(x + 0.777777778)(x + 0.777777778) = 1.3827160498

Calculate the square root of the right side: 1.175889472

Break this problem into two subproblems by setting 
(x + 0.777777778) equal to 1.175889472 and -1.175889472.

Subproblem 1

x + 0.777777778 = 1.175889472 Simplifying x + 0.777777778 = 1.175889472 Reorder the terms: 0.777777778 + x = 1.175889472 Solving 0.777777778 + x = 1.175889472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 1.175889472 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 1.175889472 + -0.777777778 x = 1.175889472 + -0.777777778 Combine like terms: 1.175889472 + -0.777777778 = 0.398111694 x = 0.398111694 Simplifying x = 0.398111694

Subproblem 2

x + 0.777777778 = -1.175889472 Simplifying x + 0.777777778 = -1.175889472 Reorder the terms: 0.777777778 + x = -1.175889472 Solving 0.777777778 + x = -1.175889472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -1.175889472 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -1.175889472 + -0.777777778 x = -1.175889472 + -0.777777778 Combine like terms: -1.175889472 + -0.777777778 = -1.95366725 x = -1.95366725 Simplifying x = -1.95366725

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.398111694, -1.95366725}

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