Question

Imani and Todd were trying to solve the equation: x^2+6x+5=8x 2 +6x+5=8x, squared, plus, 6, x, plus, 5, equals, 8 Imani said, "I can factor the left-hand side into (x+1)(x+5)(x+1)(x+5)left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, plus, 5, right parenthesis, so I'll solve using the zero product property." Todd said, "I can solve by completing the square. If I add 444 to each side, I can rewrite the equation as (x+3)^2=12(x+3) 2 =12left parenthesis, x, plus, 3, right parenthesis, squared, equals, 12." Whose solution strategy would work? Choose 1 answer: Choose 1 answer:

Answer 1

only todd i got it from khan

Explanation:

Answer 2

Todd's

Explanation:

Given the expression x^2+6x+5=8, we are to determine which whether Imani or Todd method will work

Imani method might not work because he hasn't written the equation in standard form before factorizing. He should have equated the expression to zero first before factorizing and finding the zeros of the expression. The equation should have been written in the form ax²+bx+c = 0 first.

For Todd, his method will work because he used the completing the square method. The value at the right hand may not necessarily be zero before applying the rule. The idea is to make the quadratic equation complete and a perfect square.

This is achieved by adding the half of coefficient of x to both sides of the expression before simplifying.

From the expression x²+6x+5 = 8 we can see that adding 4 to both sides will make the quadratic equation on the left a perfect square.

x²+6x+5= 8

x²+6x+5+4= 8 +4

x²+6x+9 = 12

x²+3x+3x+9 = 12

x(x+3)+3(x+3) = 12

(x+3)(x+3) = 12

(x+3)² = 12

We can see that the expression at the left hand is now a perfect square. Hence Todd solution strategy will work