Dimitri is solving the following equation for x. 2x^(2)-7=33 His first few steps are given below. 2x^(2)=40 x^(2)=20 x=+-sqrt20 Is it necessary for Dimitri to check his answers for extraneous solutions? Choose 1 answer: (A) Yes (B) No

Isolate x^2 term: Dimitri is solving the equation 2x^2 - 7 = 33 for x. The first step is to isolate the x^2 term by adding 7 to both sides of the equation. Calculation: 2x^2 - 7 + 7 = 33 + 7 2x^2 = 40Divide by 2: Next, Dimitri divides both sides of the equation by 2 to solve for x^2. Calculation: 2x^2 / 2 = 40 / 2 x^2 = 20Take square root: Dimitri then takes the square root of both sides to solve for x. Since the square root has both a positive and negative solution, he writes x as plus or minus the square root of 20. Calculation: x = ±√20Simplify square root: Dimitri simplifies √20 to √(4*5) to make it easier to take the square root. Calculation: x = ±√(4*5) = ±2√5Check for extraneous solutions: Now, we need to answer the ＂Is it necessary for Dimitri to check his answers for extraneous solutions?＂ Since Dimitri has performed operations that are valid for all real numbers (adding, subtracting, multiplying, dividing by a non-zero number, and taking even roots of positive numbers), there is no need to check for extraneous solutions. The operations he used do not introduce any solutions that weren't already present in the original equation.

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Dimitri is solving the following equation for
x.

2x^(2)-7=33
His first few steps are given below.

2x^(2)=40

x^(2)=20

x=+-sqrt20
Is it necessary for Dimitri to check his answers for extraneous solutions?
Choose 1 answer:
(A) Yes
(B) No

Dimitri is solving the following equation for $x$ . $\newline$ $2 x^{2}-7=33$ $\newline$ His first few steps are given below. $\newline$ $2 x^{2}=40$ $\newline$ $x^{2}=20$ $\newline$ $x= \pm \sqrt{20}$ $\newline$ Is it necessary for Dimitri to check his answers for extraneous solutions? $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) No

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Math Problems

Algebra 1

Solve a system of equations using any method: word problems

Full solution

Q. Dimitri is solving the following equation for

x

\newline

2 x^{2}-7=33

\newline

His first few steps are given below.

\newline

2 x^{2}=40

\newline

x^{2}=20

\newline

x= \pm \sqrt{20}

\newline

Is it necessary for Dimitri to check his answers for extraneous solutions?

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B) No

Isolate $x^2$ term: Dimitri is solving the equation $2x^2 - 7 = 33$ for $x$ . The first step is to isolate the $x^2$ term by adding $7$ to both sides of the equation. $\newline$ Calculation: $2x^2 - 7 + 7 = 33 + 7$ $\newline$ $2x^2 = 40$
Divide by $2$ : Next, Dimitri divides both sides of the equation by $2$ to solve for $x^2$ . $\newline$ Calculation: $\frac{2x^2}{2} = \frac{40}{2}$ $\newline$ $x^2 = 20$
Take square root: Dimitri then takes the square root of both sides to solve for $x$ . Since the square root has both a positive and negative solution, he writes $x$ as plus or minus the square root of $20$ . $\newline$ Calculation: $x = \pm\sqrt{20}$
Simplify square root: Dimitri simplifies $\sqrt{20}$ to $\sqrt{(4\cdot5)}$ to make it easier to take the square root. $\newline$ Calculation: $x = \pm\sqrt{(4\cdot5)} = \pm2\sqrt{5}$
Check for extraneous solutions: Now, we need to answer the ＂Is it necessary for Dimitri to check his answers for extraneous solutions?＂ Since Dimitri has performed operations that are valid for all real numbers (adding, subtracting, multiplying, dividing by a non-zero number, and taking even roots of positive numbers), there is no need to check for extraneous solutions. The operations he used do not introduce any solutions that weren't already present in the original equation.