Question

solve by completing the square method x^2-5x+4=0​

Answer 1

Answer:

x² - 5x + 4 = 0

=> x² -5x = - 4

=> x² - 5x +(5/2)² = -4 + (5/2)²

=> x² - 5x + 25/4 = - 4 + 25/4

=> x² - 5x + 25/4 = (-16 + 25)/4

=> (x - 5/2)² = 9/4

=> x - 5/2 = √(9/4)

=> x - 5/2 = ± 3/2

=> x = ± 3/2 + 5/2

=> x = 3/2 + 5/2 = 4

=> x = -3/2 + 5/2 = 2/2 = 1

therefore x = 4 and x = 1

Answer 2

The answer is; x = -1 x = 4

GIVEN

Quadratic equation; x² - 5x + 4 = 0

TO FIND

The roots of x by completing the square method.

SOLUTION

We can simply solve the above problem as follows;

We know that to solve a quadratic equation by completing the square method, the equation should be in the standard form;

x² + bx = c

Therefore,

x²-5x+4 = 0

Can be written as;

x² - 5x = -4

Now, Dividing the coefficient of x by 2 to get 5/2, then add the square of 5/2 to both side of the equation. This will make the LHS a perfect square.

$x^{2} - \frac{5}{2}x +( \frac{5}{2} )^{2} = - 4 +( \frac{25}{4} )$

$= x^{2} - \frac{5}{2}x +( \frac{25}{4} ) = - 4 +( \frac{25}{4} )$

Solving the RHS

$= x^{2} - \frac{5}{2}x +( \frac{25}{4} ) = \frac{9}{4}$

Factorising LHS;

$= (x + \frac{5}{2}) ^{2} = \frac{9}{4}$

Taking square roots of LHS and RHS;

$= \sqrt{ (x + \frac{5}{2})^{2} } = \sqrt{ \frac{9}{4} }$

Simplifying,

$x + \frac{5}{2} = ± \frac{3}{2}$

x = 3/2 + 5/2

= 8/2

x = 4

x = -3/2 + 5/2

x = -1

Hence, The answer is; x = -1 x = 4

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