Question

question
use the quadratic formula to solve. express your answer in simplest form.
$7w^2 + 2w - 3 = -w^2$

Explanation:

Step1: Rewrite the equation in standard form

First, we need to rewrite the given equation \(7w^{2}+2w - 3=-w^{2}\) in the standard quadratic form \(ax^{2}+bx + c = 0\) (here we use \(w\) instead of \(x\)). We add \(w^{2}\) to both sides of the equation:

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So, \(a = 8\), \(b=2\), and \(c=-3\).

Step2: Apply the quadratic formula

The quadratic formula is given by \(w=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). Substitute \(a = 8\), \(b = 2\), and \(c=-3\) into the formula:
First, calculate the discriminant \(\Delta=b^{2}-4ac\):

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Then, find the values of \(w\):

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Step3: Find the two solutions

We have two cases for the \(\pm\) sign:

• Case 1: When we take the plus sign:

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• Case 2: When we take the minus sign:

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Answer:

\(w=\frac{1}{2}\) or \(w =-\frac{3}{4}\)