Question

The question in the photo below.

Answer 1

A. { -5,2}

Explanation:

In order t find the solution set of the equation x² + 3x - 4 = 6 , we need to first move all terms to one side of the equation and then solve for x.

Here's the equation:

`\sf x^2 + 3x - 4 - 6 = 0`

Now, simplify the equation:

`\sf x^2 + 3x - 10 = 0`

To solve this quadratic equation, we can use the quadratic formula:

`\sf x = (-b \pm √(b^2 - 4ac))/(2a)`

where

• a is the coefficient of a², which is 1,
• b is the coefficient of x, which is 3
• c is the constant term, which is -10.

Now

Substitute these values into the quadratic formula and solve for x.

`\begin{aligned} x & = (-3 \pm √(3^2 - 4(1)(-10)))/(2(1)) \\\\& = (-3 \pm √(9+40))/(2) \\\\ & = (-3 \pm √(49))/(2) \\\\ &=(-3 \pm 7)/(2) \end{aligned}`

Now, we have two possible solutions:

When positive

`\begin{aligned} x &= (-3 + 7)/(2) \\\\ &= (4)/(2) \\\\ & = 2 \end{aligned}`

When negative

`\begin{aligned} x &= (-3 - 7)/(2) \\\\ &= (-10)/(2) \\\\ & = -5 \end{aligned}`

Therefore, the solution set of the equation is A. { -5,2}.