Create a list of steps, in order, that will solve the following equation. (1)/(2)(x+5)^(2)+2=42.5 Solution steps: Add 2 to both sides Multiply both sides by 2 Multiply both sides by (1)/(2) Subtract 2 from both sides Subtract 5 from both sides Square both sides Take the

Isolate the variable: Step 1: Subtract 2 from both sides to isolate the term with the variable. (1)/(2)(x+5)^(2) + 2 - 2 = 42.5 - 2 (1)/(2)(x+5)^(2) = 40.5 Eliminate the fraction: Step 2: Multiply both sides by 2 to eliminate the fraction. 2 * (1)/(2)(x+5)^(2) = 40.5 * 2 (x+5)^(2) = 81 Solve for x+5: Step 3: Take the square root of both sides to solve for x+5. sqrt((x+5)^(2)) = ± sqrt(81) x + 5 = ± 9 Solve for x: Step 4: Subtract 5 from both sides to solve for x. x + 5 - 5 = ± 9 - 5 x = 4 or x = -14 Final answer: Step 5: Write the final answer with the solutions in order from least to greatest. The solutions are x = -14 and x = 4.

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Create a list of steps, in order, that will solve the following equation.

(1)/(2)(x+5)^(2)+2=42.5
Solution steps:
Add 2 to both sides
Multiply both sides by 2
Multiply both sides by
(1)/(2)
Subtract 2 from both sides
Subtract 5 from both sides
Square both sides
Take the

Create a list of steps, in order, that will solve the following equation. $\newline$ $\frac{1}{2}(x+5)^{2}+2=42.5$ $\newline$ Solution steps: $\newline$ - Add $2$ to both sides $\newline$ - Multiply both sides by $2$ $\newline$ - Multiply both sides by $\frac{1}{2}$ $\newline$ - Subtract $2$ from both sides $\newline$ - Subtract $5$ from both sides $\newline$ - Square both sides $\newline$ - Take the

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Math Problems

Algebra 2

Solve a quadratic equation using square roots

Full solution

Q. Create a list of steps, in order, that will solve the following equation.

\newline

\frac{1}{2}(x+5)^{2}+2=42.5

\newline

Solution steps:

\newline

- Add

2

to both sides

\newline

- Multiply both sides by

2

\newline

- Multiply both sides by

\frac{1}{2}

\newline

- Subtract

2

from both sides

\newline

- Subtract

5

from both sides

\newline

- Square both sides

\newline

- Take the

Isolate the variable: Step $1$ : Subtract $2$ from both sides to isolate the term with the variable. $\newline$ $(\frac{1}{2})(x+5)^{2} + 2 - 2 = 42.5 - 2$ $\newline$ $(\frac{1}{2})(x+5)^{2} = 40.5$
Eliminate the fraction: Step $2$ : Multiply both sides by $2$ to eliminate the fraction. $\newline$ $2 \times \frac{1}{2}(x+5)^{2} = 40.5 \times 2$ $\newline$ $(x+5)^{2} = 81$
Solve for $x+5$ : Step $3$ : Take the square root of both sides to solve for $x+5$ . $\sqrt{(x+5)^{2}} = \pm \sqrt{81}$ $x + 5 = \pm 9$
Solve for x: Step $4$ : Subtract $5$ from both sides to solve for $x$ . $\newline$ $x +$ $5$ - $5$ = \pm $9$ - $5$ $\newline$ $x =$ $4$ or $x =$ $-14$
Final answer: Step $5$ : Write the final answer with the solutions in order from least to greatest. $\newline$ The solutions are $x = -14$ and $x = 4$ .