This is Josh’s work and solution for the equation x^2-6x-7=0:
x^2-6x-7=0
x^2-6x=7
x^2-6x+9=7+9
(x-3)^2=16
√(x-3)^2 )=±√16
x-3=± 4
x=-3±4

x=-3+4 x=-3-4
x=1 x=-7

Is Josh’s solution correct? Explain.

Step-by-step explanation:

the solution is right

x^2-6x-7=0:

x^2-6x-7=0 (add 7 to both sides)

x^2-6x=7

x^2-6x+9=7+9  (the coefficient of x² will be used to divide all sides)for here its 1, it will remain same ,

then we get the coefficient of x, divide it by 2 and square it and add it to both sides

which is like these

x²-6x=7

the coefficient of x is -6

-6/2 = -3, square it (-3)² = 9

then add 9 to both sides

x^2-6x+9=7+9

simplifiy the squares on the left hand side

x²+9 = (x-3)²

(x-3)^2=16

√(x-3)^2 )=±√16

x-3=± 4

x=-3±4

then simplify each sign

x=-3+4            x=-3-4

x=1                   x=-7

his solution was incorrect.

Step-by-step explanation:

The given equation is expressed as

x² - 6x - 7 = 0

Josh was applying the method of completing the square. Since the coefficient of the first term is 1, the next step he took was to add the square of the coefficient of x to the left hand side and the right hand side of the equation which is correct.

After adding, he took the square root of the left hand side and the right hand side of the equation which is also correct.

Finally, he made a mistake by adding - 3 instead of 3 to the left hand side and the right hand side of the equation. Therefore, his solution is incorrect

The right step is

x - 3 = ± 4

x = 3 ± 4

x = 3 + 4 or x = 3 - 4

x = 7 or x = - 1

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.