Question

Nathaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below.



What are the solutions to the equation?

x = –1, 6
x = –6, 1
x = –22, 27
x = –27, 22

Answer 1

Answer:

x= -6,1

Step-by-step explanation:

The Given Equation is $x^{2} +5x-6 =0$   ...............(i)

Now we Know that Quadratic formula is

$x = \frac{-b+\sqrt{b^{2}-4ac}}{2a}$  ............(ii) and  

$x = \frac{-b-\sqrt{b^{2}-4ac}}{2a}$   ..............(iii)

In the given equation

a= 1 , b= 5 , c= -6

For the first value of x Putting these in equation (ii) gives

$x = \frac{-5+\sqrt{5^{2}-4(1)(-6)}}{2(1)}$

$x = \frac{-5+\sqrt{49}}{2}$

$x = \frac{-5+7}{2}$

$x = \frac{2}{2}$

x= 1

so one value of x = 1

Now for the second value we will put the values in eqaution (ii) which gives us

$x = \frac{-5-\sqrt{5^{2}-4(1)(-6)}}{2(1)}$

$x = \frac{-5-\sqrt{49}}{2}$

$x = \frac{-5-7}{2}$

$x = \frac{-12}{2}$

x= -6

so second value of x = -6

So the solution to equation is x= -6,1

Answer 2

For this case we have the following polynomial:

The quadratic formula is given by:

Substituting values in the given equation we have:

Rewriting we have:

Therefore, the solutions are given by:

Solution 1:

Solution 2:

Answer:

he solutions to the equation are:

x = –6, 1

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