Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.

Question

5-2x^2= -15

Answer 1

To solve the equation \( 5 - 2x^2 = -15 \) using inverse operations, we will isolate \( x^2 \) step by step. Let's proceed:

1. Subtract 5 from both sides: \[ 5 - 2x^2 - 5 = -15 - 5 \] This simplifies to: \[ -2x^2 = -20 \]

2. Divide both sides by -2: \[ \frac{-2x^2}{-2} = \frac{-20}{-2} \] This simplifies to: \[ x^2 = 10 \]

3. Take the square root of both sides: Remember to consider both the positive and negative roots. \[ x = \pm \sqrt{10} \] Thus, the solutions are: \[ x = \sqrt{10} \quad \text{and} \quad x = -\sqrt{10} \]

Now, let's check the solutions by substituting \( x \) back into the original equation.

Checking the solutions

For \( x = \sqrt{10} \): \[ 5 - 2(\sqrt{10})^2 = 5 - 2(10) = 5 - 20 = -15 \]

For \( x = -\sqrt{10} \): \[ 5 - 2(-\sqrt{10})^2 = 5 - 2(10) = 5 - 20 = -15 \]

In both cases, we find that the original equation holds true.

Final Answer

The solutions to the equation \( 5 - 2x^2 = -15 \) are: \[ \boxed{\sqrt{10}} \quad \text{and} \quad \boxed{-\sqrt{10}} \]

Answer 2

can you do it without all the symbols and slashes

Answer 3

Sure! Let's solve the equation step by step using simple language without symbols and slashes.

We start with the equation:

Step 1: The equation is
5 minus 2 times x squared equals negative 15.

Step 2: To isolate the term with x, first subtract 5 from both sides.
This means we take away 5 from both sides of the equation.
So we have:
-2 times x squared equals negative 20.

Step 3: Now, we need to remove the negative 2 in front of x squared.
We can do this by dividing both sides of the equation by negative 2.
This simplifies to:
x squared equals 10.

Step 4: Next, we take the square root of both sides to solve for x.
This gives us:
x equals the square root of 10, or x equals negative square root of 10.

So, the solutions are:
x equals square root of 10
and
x equals negative square root of 10.

Final Step: Let's check our solutions.

For x equals square root of 10:
Substituting into the original equation:
5 minus 2 times (square root of 10) squared equals negative 15.
Calculating this, we find that it holds true.

For x equals negative square root of 10:
We substitute again into the original equation:
5 minus 2 times (negative square root of 10) squared equals negative 15.
This also holds true.

In conclusion, we have verified our solutions. The final answers are:

x equals square root of 10 and x equals negative square root of 10.