49x^2-69x+20=7x^2-8

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Solution for 49x^2-69x+20=7x^2-8 equation:


Simplifying
49x2 + -69x + 20 = 7x2 + -8

Reorder the terms:
20 + -69x + 49x2 = 7x2 + -8

Reorder the terms:
20 + -69x + 49x2 = -8 + 7x2

Solving
20 + -69x + 49x2 = -8 + 7x2

Solving for variable 'x'.

Reorder the terms:
20 + 8 + -69x + 49x2 + -7x2 = -8 + 7x2 + 8 + -7x2

Combine like terms: 20 + 8 = 28
28 + -69x + 49x2 + -7x2 = -8 + 7x2 + 8 + -7x2

Combine like terms: 49x2 + -7x2 = 42x2
28 + -69x + 42x2 = -8 + 7x2 + 8 + -7x2

Reorder the terms:
28 + -69x + 42x2 = -8 + 8 + 7x2 + -7x2

Combine like terms: -8 + 8 = 0
28 + -69x + 42x2 = 0 + 7x2 + -7x2
28 + -69x + 42x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
28 + -69x + 42x2 = 0

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

Divide each side by '42'.
0.6666666667 + -1.642857143x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -1.642857143x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -1.642857143x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -1.642857143x + x2 = 0 + -0.6666666667
-1.642857143x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-1.642857143x + x2 = -0.6666666667

The x term is -1.642857143x.  Take half its coefficient (-0.8214285715).
Square it (0.6747448981) and add it to both sides.

Add '0.6747448981' to each side of the equation.
-1.642857143x + 0.6747448981 + x2 = -0.6666666667 + 0.6747448981

Reorder the terms:
0.6747448981 + -1.642857143x + x2 = -0.6666666667 + 0.6747448981

Combine like terms: -0.6666666667 + 0.6747448981 = 0.0080782314
0.6747448981 + -1.642857143x + x2 = 0.0080782314

Factor a perfect square on the left side:
(x + -0.8214285715)(x + -0.8214285715) = 0.0080782314

Calculate the square root of the right side: 0.089878982

Break this problem into two subproblems by setting 
(x + -0.8214285715) equal to 0.089878982 and -0.089878982.

Subproblem 1

x + -0.8214285715 = 0.089878982 Simplifying x + -0.8214285715 = 0.089878982 Reorder the terms: -0.8214285715 + x = 0.089878982 Solving -0.8214285715 + x = 0.089878982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8214285715' to each side of the equation. -0.8214285715 + 0.8214285715 + x = 0.089878982 + 0.8214285715 Combine like terms: -0.8214285715 + 0.8214285715 = 0.0000000000 0.0000000000 + x = 0.089878982 + 0.8214285715 x = 0.089878982 + 0.8214285715 Combine like terms: 0.089878982 + 0.8214285715 = 0.9113075535 x = 0.9113075535 Simplifying x = 0.9113075535

Subproblem 2

x + -0.8214285715 = -0.089878982 Simplifying x + -0.8214285715 = -0.089878982 Reorder the terms: -0.8214285715 + x = -0.089878982 Solving -0.8214285715 + x = -0.089878982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8214285715' to each side of the equation. -0.8214285715 + 0.8214285715 + x = -0.089878982 + 0.8214285715 Combine like terms: -0.8214285715 + 0.8214285715 = 0.0000000000 0.0000000000 + x = -0.089878982 + 0.8214285715 x = -0.089878982 + 0.8214285715 Combine like terms: -0.089878982 + 0.8214285715 = 0.7315495895 x = 0.7315495895 Simplifying x = 0.7315495895

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9113075535, 0.7315495895}

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