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Use the cards below to create a list of steps, in order, that will solve the following equation.

3(x+6)^(2)=75
Solution steps:
Add 6 to both sides
Divide both sides by 3
Divide both sides by 
(1)/(3)
Subtract 6 from both sides
Square both sides
Take the square root of both sides

Use the cards below to create a list of steps, in order, that will solve the following equation.\newline3(x+6)2=753(x+6)^{2}=75\newlineSolution steps:\newlineAdd 6 to both sides\text{Add } 6 \text{ to both sides}\newlineDivide both sides by 3\text{Divide both sides by } 3\newlineDivide both sides by 13\text{Divide both sides by } \frac{1}{3}\newlineSubtract 6 from both sides\text{Subtract } 6 \text{ from both sides}\newlineSquare both sides\text{Square both sides}\newlineTake the square root of both sides\text{Take the square root of both sides}

Full solution

Q. Use the cards below to create a list of steps, in order, that will solve the following equation.\newline3(x+6)2=753(x+6)^{2}=75\newlineSolution steps:\newlineAdd 6 to both sides\text{Add } 6 \text{ to both sides}\newlineDivide both sides by 3\text{Divide both sides by } 3\newlineDivide both sides by 13\text{Divide both sides by } \frac{1}{3}\newlineSubtract 6 from both sides\text{Subtract } 6 \text{ from both sides}\newlineSquare both sides\text{Square both sides}\newlineTake the square root of both sides\text{Take the square root of both sides}
  1. Isolate squared term: First, we need to isolate the squared term on one side of the equation. To do this, we divide both sides by 33.\newlineCalculation: 3(x+6)2=75(x+6)2=753(x+6)2=253(x+6)^{2} = 75 \Rightarrow (x+6)^{2} = \frac{75}{3} \Rightarrow (x+6)^{2} = 25
  2. Take square root: Next, we take the square root of both sides to solve for x+6x+6. Remember that taking the square root of both sides introduces a plus/minus (x\sqrt{\phantom{x}} can be + or -).\newlineCalculation: (x+6)2=±25x+6=±5\sqrt{(x+6)^{2}} = \pm\sqrt{25} \Rightarrow x+6 = \pm5
  3. Isolate xx: Now, we need to isolate xx by subtracting 66 from both sides of the equation.\newlineCalculation: x+6=±5x=±56x=6+5x+6 = \pm5 \Rightarrow x = \pm5 - 6 \Rightarrow x = -6 + 5 or x=65x = -6 - 5
  4. Simplify expressions: Finally, we simplify the expressions to find the two possible values for xx.\newlineCalculation: x=6+5x=1x = -6 + 5 \Rightarrow x = -1 and x=65x=11x = -6 - 5 \Rightarrow x = -11

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