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# Algebra

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If (w + 13)^2 = (3w + 7)(2w + 5), solve for w.

Jan 24, 2022

#1
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First we open parenthesis.

$$w^2 + 26w + 169 = (3w + 7)(2w + 5)$$

Then we open parenthesis on the right side of the equation.

$$w^2 + 26w + 169 = 6w^2 +29w + 35$$

Then we have to combine like terms.

$$5w^2 + 3w -134 = 0$$

Now we can use the quadratic formula: w = $$-b {+\over} \sqrt{b^2 - 4ac}\over2a$$ where a is the coefficient of $$w^2$$, b is the coefficient of w, and c is the constant.

Now to plug in the values into the formula: we get

w = $$-3 {+\over}\sqrt{2689}\over10$$

Jan 24, 2022