7x^2=9-8x

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Solution for 7x^2=9-8x equation:


Simplifying
7x2 = 9 + -8x

Solving
7x2 = 9 + -8x

Solving for variable 'x'.

Reorder the terms:
-9 + 8x + 7x2 = 9 + -8x + -9 + 8x

Reorder the terms:
-9 + 8x + 7x2 = 9 + -9 + -8x + 8x

Combine like terms: 9 + -9 = 0
-9 + 8x + 7x2 = 0 + -8x + 8x
-9 + 8x + 7x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-9 + 8x + 7x2 = 0

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

Divide each side by '7'.
-1.285714286 + 1.142857143x + x2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + 1.142857143x + 1.285714286 + x2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + 1.142857143x + x2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + 1.142857143x + x2 = 0 + 1.285714286
1.142857143x + x2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
1.142857143x + x2 = 1.285714286

The x term is 1.142857143x.  Take half its coefficient (0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
1.142857143x + 0.3265306123 + x2 = 1.285714286 + 0.3265306123

Reorder the terms:
0.3265306123 + 1.142857143x + x2 = 1.285714286 + 0.3265306123

Combine like terms: 1.285714286 + 0.3265306123 = 1.6122448983
0.3265306123 + 1.142857143x + x2 = 1.6122448983

Factor a perfect square on the left side:
(x + 0.5714285715)(x + 0.5714285715) = 1.6122448983

Calculate the square root of the right side: 1.26974206

Break this problem into two subproblems by setting 
(x + 0.5714285715) equal to 1.26974206 and -1.26974206.

Subproblem 1

x + 0.5714285715 = 1.26974206 Simplifying x + 0.5714285715 = 1.26974206 Reorder the terms: 0.5714285715 + x = 1.26974206 Solving 0.5714285715 + x = 1.26974206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + x = 1.26974206 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = 1.26974206 + -0.5714285715 x = 1.26974206 + -0.5714285715 Combine like terms: 1.26974206 + -0.5714285715 = 0.6983134885 x = 0.6983134885 Simplifying x = 0.6983134885

Subproblem 2

x + 0.5714285715 = -1.26974206 Simplifying x + 0.5714285715 = -1.26974206 Reorder the terms: 0.5714285715 + x = -1.26974206 Solving 0.5714285715 + x = -1.26974206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + x = -1.26974206 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = -1.26974206 + -0.5714285715 x = -1.26974206 + -0.5714285715 Combine like terms: -1.26974206 + -0.5714285715 = -1.8411706315 x = -1.8411706315 Simplifying x = -1.8411706315

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6983134885, -1.8411706315}

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