4x^2=20x+9

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Solution for 4x^2=20x+9 equation:


Simplifying
4x2 = 20x + 9

Reorder the terms:
4x2 = 9 + 20x

Solving
4x2 = 9 + 20x

Solving for variable 'x'.

Reorder the terms:
-9 + -20x + 4x2 = 9 + 20x + -9 + -20x

Reorder the terms:
-9 + -20x + 4x2 = 9 + -9 + 20x + -20x

Combine like terms: 9 + -9 = 0
-9 + -20x + 4x2 = 0 + 20x + -20x
-9 + -20x + 4x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
-9 + -20x + 4x2 = 0

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

Divide each side by '4'.
-2.25 + -5x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -5x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -5x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -5x + x2 = 0 + 2.25
-5x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-5x + x2 = 2.25

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 2.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 2.25 + 6.25

Combine like terms: 2.25 + 6.25 = 8.5
6.25 + -5x + x2 = 8.5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.915475947 and -2.915475947.

Subproblem 1

x + -2.5 = 2.915475947 Simplifying x + -2.5 = 2.915475947 Reorder the terms: -2.5 + x = 2.915475947 Solving -2.5 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.915475947 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.915475947 + 2.5 x = 2.915475947 + 2.5 Combine like terms: 2.915475947 + 2.5 = 5.415475947 x = 5.415475947 Simplifying x = 5.415475947

Subproblem 2

x + -2.5 = -2.915475947 Simplifying x + -2.5 = -2.915475947 Reorder the terms: -2.5 + x = -2.915475947 Solving -2.5 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.915475947 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.915475947 + 2.5 x = -2.915475947 + 2.5 Combine like terms: -2.915475947 + 2.5 = -0.415475947 x = -0.415475947 Simplifying x = -0.415475947

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.415475947, -0.415475947}

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