7x^2-24=8x

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Solution for 7x^2-24=8x equation:


Simplifying
7x2 + -24 = 8x

Reorder the terms:
-24 + 7x2 = 8x

Solving
-24 + 7x2 = 8x

Solving for variable 'x'.

Reorder the terms:
-24 + -8x + 7x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-24 + -8x + 7x2 = 0

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

Divide each side by '7'.
-3.428571429 + -1.142857143x + x2 = 0

Move the constant term to the right:

Add '3.428571429' to each side of the equation.
-3.428571429 + -1.142857143x + 3.428571429 + x2 = 0 + 3.428571429

Reorder the terms:
-3.428571429 + 3.428571429 + -1.142857143x + x2 = 0 + 3.428571429

Combine like terms: -3.428571429 + 3.428571429 = 0.000000000
0.000000000 + -1.142857143x + x2 = 0 + 3.428571429
-1.142857143x + x2 = 0 + 3.428571429

Combine like terms: 0 + 3.428571429 = 3.428571429
-1.142857143x + x2 = 3.428571429

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 = 3.428571429 + 0.3265306123

Reorder the terms:
0.3265306123 + -1.142857143x + x2 = 3.428571429 + 0.3265306123

Combine like terms: 3.428571429 + 0.3265306123 = 3.7551020413
0.3265306123 + -1.142857143x + x2 = 3.7551020413

Factor a perfect square on the left side:
(x + -0.5714285715)(x + -0.5714285715) = 3.7551020413

Calculate the square root of the right side: 1.937808567

Break this problem into two subproblems by setting 
(x + -0.5714285715) equal to 1.937808567 and -1.937808567.

Subproblem 1

x + -0.5714285715 = 1.937808567 Simplifying x + -0.5714285715 = 1.937808567 Reorder the terms: -0.5714285715 + x = 1.937808567 Solving -0.5714285715 + x = 1.937808567 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 = 1.937808567 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.937808567 + 0.5714285715 x = 1.937808567 + 0.5714285715 Combine like terms: 1.937808567 + 0.5714285715 = 2.5092371385 x = 2.5092371385 Simplifying x = 2.5092371385

Subproblem 2

x + -0.5714285715 = -1.937808567 Simplifying x + -0.5714285715 = -1.937808567 Reorder the terms: -0.5714285715 + x = -1.937808567 Solving -0.5714285715 + x = -1.937808567 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 = -1.937808567 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.937808567 + 0.5714285715 x = -1.937808567 + 0.5714285715 Combine like terms: -1.937808567 + 0.5714285715 = -1.3663799955 x = -1.3663799955 Simplifying x = -1.3663799955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.5092371385, -1.3663799955}

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