# How to solve$f(x) = -0.7x^2+2x+3$ where $f(x) = 2$ [closed]

I tried the factoring method but was unable to factor it. I also used the quadratic formula but am not getting any of the choices listed below.

The directions are to "Solve the equation to four decimal places" f(x) = -0.7x^2+2x+3 where f(x) = 2

The choices are: A) No solution B) 3.2912 C) -0.4341 D) -0.4341, 3.2912

Thanks for help. I mistyped the problem before :x. Regardless, I still am not getting any of the choices as an answer.

## closed as off-topic by user21820, Cesareo, Christian Blatter, Archer, GNUSupporter 8964民主女神 地下教會Apr 11 at 15:05

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• $-0.7x^2+2x+3 = 2$. Use the solution form for a quadratic equation. – David G. Stork Feb 7 at 1:03

Just apply the quadratic formula.

$$-0.7x^2+2x+3=2$$ means $$-0.7x^2+2x+1=0$$

Now $$a=-0.7, b=2, c=3$$

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\to\dfrac{-2\pm\sqrt{4-4(-0.7)(3)}}{2(-0.7)}=-0.4340,3.29120$$

Answer is $$D$$

It looks like you have confusion where you can use the quadratic formula.

Anytime you have the form $$Ax^2+Bx+C=0$$, you may use it.

• That was exactly my misunderstanding... Thank you for the help! – Alektorophobiae Feb 7 at 1:14
• You're welcome! So remember you must always have one side as 0 if you wish to use the formula! – K Split X Feb 7 at 1:32

Hint:

$$f(x)=-0.7x^2+2x+3=2$$

$$\implies0.7x^2-2x-1=0$$

Now use the formula $$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$

• Are you able to do that? I thought the problem was saying that f(x) = 2 and not x = 2? – Alektorophobiae Feb 7 at 1:01
• @Alektorophobiae Use the quadratic formula – Key Flex Feb 7 at 1:03
• It is saying $f(x) = 2$! So $-0.7x^2 + 2x + 3 =2$. We need to solve for $x$. And Key Flex answer is telling you exactly how to do if. If $-0.7x^2 + 2x + 3 = 2$ then $0.7x2 -2x -1 = 0$ and we can apply the quadratic formula to solve. – fleablood Feb 7 at 1:06
• Why Downvote? Is anything wrong in my answer? – Key Flex Feb 7 at 1:09
• @fleablood he originally said it how I said but he rephrased.. I did do the quadratic formula but I am not getting any of the possible solutions. I do appreciate the help though Key Flex. I'm not sure if I am erring in my arithmetic.. – Alektorophobiae Feb 7 at 1:10

I’m sure that this problem was meant to force you to practice using the quadratic formula, but since you’re presented with possible solutions, one of which combines two of the others, before plunging into working out the solution for yourself, roll the dice: plug the given values into $$f$$ and see what you get. To four decimal places, both $$f(3.2912)$$ and $$f(-0.4341)$$ are equal to $$2$$, so the correct answer must be D.

Use the quadratic equation on $$-0.7 x^2 + 2 x + 3 = 2$$ to find:

$$x = -0.434058$$, or $$3.2912$$ 