8-3x^2=7x

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Solution for 8-3x^2=7x equation:


Simplifying
8 + -3x2 = 7x

Solving
8 + -3x2 = 7x

Solving for variable 'x'.

Reorder the terms:
8 + -7x + -3x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
8 + -7x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-2.666666667 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.333333333x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 2.333333333x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + 2.666666667
2.333333333x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
2.333333333x + x2 = 2.666666667

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 2.666666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 2.666666667 + 1.361111112

Combine like terms: 2.666666667 + 1.361111112 = 4.027777779
1.361111112 + 2.333333333x + x2 = 4.027777779

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 4.027777779

Calculate the square root of the right side: 2.00693243

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 2.00693243 and -2.00693243.

Subproblem 1

x + 1.166666667 = 2.00693243 Simplifying x + 1.166666667 = 2.00693243 Reorder the terms: 1.166666667 + x = 2.00693243 Solving 1.166666667 + x = 2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 2.00693243 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 2.00693243 + -1.166666667 x = 2.00693243 + -1.166666667 Combine like terms: 2.00693243 + -1.166666667 = 0.840265763 x = 0.840265763 Simplifying x = 0.840265763

Subproblem 2

x + 1.166666667 = -2.00693243 Simplifying x + 1.166666667 = -2.00693243 Reorder the terms: 1.166666667 + x = -2.00693243 Solving 1.166666667 + x = -2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -2.00693243 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -2.00693243 + -1.166666667 x = -2.00693243 + -1.166666667 Combine like terms: -2.00693243 + -1.166666667 = -3.173599097 x = -3.173599097 Simplifying x = -3.173599097

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.840265763, -3.173599097}

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