Questions: Solve: 7(x+5)^2-3=340

Solution Steps

To solve the equation \(7(x+5)^{2} - 3 = 340\), we will first isolate the squared term by adding 3 to both sides and then dividing by 7. Next, we will take the square root of both sides to solve for \(x+5\). Finally, we will subtract 5 from both sides to solve for \(x\).

To solve the equation \(7(x+5)^{2} - 3 = 340\), we will follow these steps:

First, we need to isolate the term that contains the square. We start by adding 3 to both sides of the equation:

\[ 7(x+5)^{2} - 3 + 3 = 340 + 3 \]

This simplifies to:

\[ 7(x+5)^{2} = 343 \]

Next, divide both sides of the equation by 7 to solve for \((x+5)^{2}\):

\[ \frac{7(x+5)^{2}}{7} = \frac{343}{7} \]

This simplifies to:

\[ (x+5)^{2} = 49 \]

To solve for \(x+5\), take the square root of both sides. Remember that taking the square root introduces both a positive and a negative solution:

\[ x+5 = \pm \sqrt{49} \]

This gives us:

\[ x+5 = \pm 7 \]

Now, solve for \(x\) by subtracting 5 from both sides for each case:

1. \(x+5 = 7\)

   \[ x = 7 - 5 = 2 \]

2. \(x+5 = -7\)

   \[ x = -7 - 5 = -12 \]

Final Answer