4x^2=20x-17

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Solution for 4x^2=20x-17 equation:


Simplifying
4x2 = 20x + -17

Reorder the terms:
4x2 = -17 + 20x

Solving
4x2 = -17 + 20x

Solving for variable 'x'.

Reorder the terms:
17 + -20x + 4x2 = -17 + 20x + 17 + -20x

Reorder the terms:
17 + -20x + 4x2 = -17 + 17 + 20x + -20x

Combine like terms: -17 + 17 = 0
17 + -20x + 4x2 = 0 + 20x + -20x
17 + -20x + 4x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
17 + -20x + 4x2 = 0

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

Divide each side by '4'.
4.25 + -5x + x2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + -5x + -4.25 + x2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + -5x + x2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + -5x + x2 = 0 + -4.25
-5x + x2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
-5x + x2 = -4.25

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 = -4.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -4.25 + 6.25

Combine like terms: -4.25 + 6.25 = 2
6.25 + -5x + x2 = 2

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.414213562 and -1.414213562.

Subproblem 1

x + -2.5 = 1.414213562 Simplifying x + -2.5 = 1.414213562 Reorder the terms: -2.5 + x = 1.414213562 Solving -2.5 + x = 1.414213562 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 = 1.414213562 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.414213562 + 2.5 x = 1.414213562 + 2.5 Combine like terms: 1.414213562 + 2.5 = 3.914213562 x = 3.914213562 Simplifying x = 3.914213562

Subproblem 2

x + -2.5 = -1.414213562 Simplifying x + -2.5 = -1.414213562 Reorder the terms: -2.5 + x = -1.414213562 Solving -2.5 + x = -1.414213562 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 = -1.414213562 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.414213562 + 2.5 x = -1.414213562 + 2.5 Combine like terms: -1.414213562 + 2.5 = 1.085786438 x = 1.085786438 Simplifying x = 1.085786438

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.914213562, 1.085786438}

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