solve each quadratic by factoring

Question

x^2+3x+35=17x-14

Answer 1

In order to solve the quadratic equation by factoring, we need to set the equation equal to zero.

Subtract 17x from both sides and add 14 to both sides

x^2 + 3x - 17x +35 + 14 = 0

Group like terms

x^2 -14x + 49 = 0

To factor, we need to find 2 products of 49 that also sum to -14 (remember to take account of the negative sign)

__ * __ = 49

__ + __ = -14

-7 * -7 =49

-7 + -7 =14

So we would factor like this:

(x-7)(x-7)=0 or (x-7)^2=0

Normally we split each factored pair in parentheses and keep it set equal to zero and solve for each separate x, but because both factored pairs within the parentheses are the same, we just solve for one:

x-7=0

x=7 is the answer

Answer 2

x² + 3x + 35 = 17x - 14

x² - 14x + 49 = 0

You want two number that add to -14 and multiply to give 49. The answer is -7 and -7:

-7 + (-7) = -14

(-7)(-7) = 49

x² - 14x + 49 = (x-7)(x-7) = (x-7)² = 0

True when x = 7.