Question

Solve for x:
(x − 2)(x + 7) = −1+2x

Answer 1

Answer:

(-3±√61)÷2

Step-by-step explanation:

First we expand the brackets to give us :

x²+5x-14 = -1 +2x

Now we make this into the quadratic format (x²+ax+b=0) by subtract -1 and 2x from both sides :

x²+3x-13 = 0

This quadratic cannot be factorized so we must use the quadratic formula :

x = $\frac{-b+\sqrt{b^{2} -4ac} }{2a}$   or   x = $\frac{-b-\sqrt{b^{2} -4ac} }{2a}$

a = 1 , b = 3 , c = -13

Now we simplify as much as possible by first substituting values known :

x = $\frac{-3+\sqrt{3^{2} -4(1)(-13)} }{2(1)}$    or   x = $\frac{-3-\sqrt{3^{2} -4(1)(-13)} }{2(1)}$

Now we evaluate the exponent :

x = $\frac{-3+\sqrt{9 -4(1)(-13)} }{2(1)}$   or     x = $\frac{-3-\sqrt{9 -4(1)(-13)} }{2(1)}$

Now we multiply the numbers :

x = $\frac{-3+\sqrt{9 +52 } }{2(1)}$    or   x = $\frac{-3-\sqrt{9 +52 } }{2(1)}$

Now we add the numbers :

x = $\frac{-3+\sqrt{61} }{2(1)}$   or   x = $\frac{-3-\sqrt{61} }{2(1)}$

Now we multiply the denominator:

x = $\frac{-3+\sqrt{61} }{2}$   or   x = $\frac{-3-\sqrt{61} }{2}$

So our final answer is (-3±√61)÷2

Hope this helped and 5 stars, a heart and brainliest please