Consider the given equation [tex]x^2-8x+14=0[/tex]
We will solve this equation by completing the square method.
Consider the coefficient of 'x', divide it by '2'. then adding and subtracting the square of this number in the given equation.
Coefficient of 'x' = -8
By dividing it by '2', we get -4
Taking the square of '-4' = 16
Adding and subtracting '16' from the given equation.
[tex]x^2-8x+14+16-16=0[/tex]
So, [tex]x^2-8x+16 = -14+16[/tex]
This equation shows one of the step used in solving the equation by completing the square method.
Therefore, option 1 is the correct answer.
For Jamal to solve the equation, [tex]x^2 - 8x + 14 = 0[/tex], by completing the square, one of the steps that could be taken is: A. [tex]\mathbf{x^2 - 8x + 16 = - 14 + 16}[/tex]
Jamal was given the equation, [tex]x^2 - 8x + 14 = 0[/tex], to solve by completing the square.
To do this, the first step would be to move the constant, 14 to the other side of the equation by subtracting 14 from both sides of the equation.
[tex]x^2 - 8x + 14 - 14 = 0 -14\\\\x^2 - 8x = -14[/tex]
The next step to take is for Jamal to add the square of half of the coefficient of x to both sides of the equation.
[tex]x^2 - 8x + 16 = - 14 + 16[/tex] (this tallies with the first option given).
Therefore, for Jamal to solve the equation, [tex]x^2 - 8x + 14 = 0[/tex], by completing the square, one of the steps that could be taken is: A. [tex]\mathbf{x^2 - 8x + 16 = - 14 + 16}[/tex]
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