Question

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

5 - 2x^2 = -15

Answer 1

To solve the equation 5 - 2x^2 = -15 using inverse operations, we need to isolate the variable x on one side of the equation.

1. Start by adding 15 to both sides of the equation to eliminate the constant term on the right side:

5 - 2x^2 + 15 = -15 + 15

20 - 2x^2 = 0

2. Next, divide both sides of the equation by -2 to isolate the x^2 term:

(20 - 2x^2) / -2 = 0 / -2

-10 + x^2 = 0

3. Now, move the constant term to the other side by adding 10 to both sides:

-10 + x^2 + 10 = 0 + 10

x^2 = 10

4. To solve for x, we need to take the square root of both sides of the equation:

√(x^2) = √(10)

x = ±√(10)

To check the solutions, substitute them back into the original equation and see if they make it true:

For x = √(10):

5 - 2(√(10))^2 = -15

5 - 2(10) = -15

5 - 20 = -15

-15 = -15 (True)

For x = -√(10):

5 - 2(-√(10))^2 = -15

5 - 2(10) = -15

5 - 20 = -15

-15 = -15 (True)

So, the solutions to the equation 5 - 2x^2 = -15 are x = √(10) and x = -√(10).

Answer 2

5-2x2=-15

Two solutions were found :

x = ± √10 = ± 3.1623

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

5-2*x^2-(-15)=0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(5 - 2x2) - -15 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

20 - 2x2 = -2 • (x2 - 10)

Trying to factor as a Difference of Squares :

3.2 Factoring: x2 - 10

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 10 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step 3 :

-2 • (x2 - 10) = 0

Step 4 :

Equations which are never true :

4.1 Solve : -2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2 Solve : x2-10 = 0

Add 10 to both sides of the equation :

x2 = 10

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 10

The equation has two real solutions

These solutions are x = ± √10 = ± 3.1623

Two solutions were found :

x = ± √10 = ± 3.1623