Question

STEP 1 of 2: consider the following quadratic equation: x^2 + 14x + 49 = 0Using the standard form ax^2 + bx + c = 0 of the given quadratic equation, factor the left hand side of the equation into two linear factors. STEP 2 of 2: x^2 + 14x + 49 = 0Solve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary. PICTURE IS OF STEP 1:

Answer 1

STEP 1: We are to factor the quadratic

`\begin{gathered} x^2+14x+49=0 \\ \end{gathered}`

This will result in two linear factors;

`\begin{gathered} x^2+14x+49=0 \\ lets\text{ get factors which multiply to give 49 and add to give 14, that is 7 twice.} \\ x^2+7x+7x+49=0 \\ x(x+7)+7(x+7)=0 \\ (x+7)(x+7)=0 \end{gathered}`

Thus, the factored form is ( x + 7)( x + 7)=0

STEP 2: We are to solve the equation by factoring,

we have already factored the equation as;

`(x+7)(x+7)=0`

For this to be true (x + 7) has to be equal to zero, i.e

`\begin{gathered} x+7=0 \\ x=-7 \end{gathered}`

Therefore x = - 7 (twice)