solve 4(x + 2)^2 = 16 using any method

[Third Degree]

Solve the equation using any appropriate method:

. . .4(x + 2)² = 16

My work:

. . .4x + 8² = 16
. . .4x + 64 = 16
. . .4x = -48
. . .x = -4

Is my work correct?

 

[Denis]

Solve the equation using any appropriate method:
. . .4(x + 2)² = 16
My work:
. . .4x + 8² = 16
. . .4x + 64 = 16
. . .4x = -48
. . .x = -4
Is my work correct?

No. But you "lucked" in 1 of the 2 solutions!

 

[stapel]

Has your class not yet covered multiplying polynomials...?

. . . . .(x + 2)²
. . . . .(x + 2)(x + 2)
. . . . .x² + 2x + 2x + 4
. . . . .x² + 4x + 4

. . . . .4(x + 2)²
. . . . .4(x² + 4x + 4)
. . . . .4x² + 16x + 16

Note that the solution to any "solving" exercise can be checked by plugging the answer back into the original problem. Checking your solution:

. . . . .x = -4:

. . . . .4([-4] + 2)²
. . . . .4(-4 + 2)²
. . . . .4(-2)²
. . . . .4(4)
. . . . .16

A series of incorrect steps arrived (luckily) at one of the correct answers. But you would likely receive no credit, since the reasoning you used will usually produce no correct answers.

Instead, try expanding the square, then multiplying by the 4, then subtracting the 16 over to the left-hand side, and solving the resulting quadratic equation. Or else just divide through by 4 and take the square root of both sides, remembering the "plus-minus" on the numerical side.

Eliz.

 

[soroban]

Hello, Third Degree!

Solve the equation using any appropriate method:

. . .\(\displaystyle 4(x\,+\,2)^2 \;= \;16\)

Take the square root of both sides:

. . . . . . \(\displaystyle \sqrt{4(x\,+\,2)^2} \;= \;\sqrt{16}\)

. . . . . . . . \(\displaystyle 2(x\,+\,2) \;=\;\pm4\)

Divide by 2: .\(\displaystyle x\,+\,2 \;=\;\pm2\)

Subtract 2: . . . .\(\displaystyle x \;=\;-2\,\pm\,2\)

Answers: \(\displaystyle \;\begin{array}{cc}x\:=\: & -2 + 2 & \:=\: & 0 \\ x\:=\: & -2 -2 & \:=\: & -4\end{array}\)

 

[Denis]

Solve the equation using any appropriate method:
. . .4(x + 2)² = 16

Well, why not divide by 4 right off the bat?

(x + 2)^2 = 4

x + 2 = +-2

x = 0 or x = -4