8x^2=20x+45

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Solution for 8x^2=20x+45 equation:


Simplifying
8x2 = 20x + 45

Reorder the terms:
8x2 = 45 + 20x

Solving
8x2 = 45 + 20x

Solving for variable 'x'.

Reorder the terms:
-45 + -20x + 8x2 = 45 + 20x + -45 + -20x

Reorder the terms:
-45 + -20x + 8x2 = 45 + -45 + 20x + -20x

Combine like terms: 45 + -45 = 0
-45 + -20x + 8x2 = 0 + 20x + -20x
-45 + -20x + 8x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
-45 + -20x + 8x2 = 0

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

Divide each side by '8'.
-5.625 + -2.5x + x2 = 0

Move the constant term to the right:

Add '5.625' to each side of the equation.
-5.625 + -2.5x + 5.625 + x2 = 0 + 5.625

Reorder the terms:
-5.625 + 5.625 + -2.5x + x2 = 0 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + -2.5x + x2 = 0 + 5.625
-2.5x + x2 = 0 + 5.625

Combine like terms: 0 + 5.625 = 5.625
-2.5x + x2 = 5.625

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 5.625 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 5.625 + 1.5625

Combine like terms: 5.625 + 1.5625 = 7.1875
1.5625 + -2.5x + x2 = 7.1875

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 7.1875

Calculate the square root of the right side: 2.680951324

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.680951324 and -2.680951324.

Subproblem 1

x + -1.25 = 2.680951324 Simplifying x + -1.25 = 2.680951324 Reorder the terms: -1.25 + x = 2.680951324 Solving -1.25 + x = 2.680951324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.680951324 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.680951324 + 1.25 x = 2.680951324 + 1.25 Combine like terms: 2.680951324 + 1.25 = 3.930951324 x = 3.930951324 Simplifying x = 3.930951324

Subproblem 2

x + -1.25 = -2.680951324 Simplifying x + -1.25 = -2.680951324 Reorder the terms: -1.25 + x = -2.680951324 Solving -1.25 + x = -2.680951324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.680951324 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.680951324 + 1.25 x = -2.680951324 + 1.25 Combine like terms: -2.680951324 + 1.25 = -1.430951324 x = -1.430951324 Simplifying x = -1.430951324

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.930951324, -1.430951324}

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