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The question in the photo below.

The question in the photo below.-example-1

1 Answer

1 vote

Answer:

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}.

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