QuestionSolve the equation $-2x^2 - 20x - 42 = 0$ by first dividing by $-2$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $-x^{} -20x -42 =0$ . We are solving for the variable $x$ .

STEP 2

The hint suggests that we should first divide the entire equation by $-2$ . This will simplify the equation and make it easier to solve.
$\frac{-2x^{2} -20x -42}{-2} = \frac{0}{-2}$

STEP 3

Divide each term in the equation by $-2$ .
$x^{2} +10x +21 =0$

STEP 4

Now, we need to solve the quadratic equation $x^{2} +10x +21 =0$ . We can do this by factoring the equation.

STEP 5

To factor the equation, we need to find two numbers that add up to $10$ and multiply to $21$ . The numbers $7$ and $3$ satisfy these conditions.

STEP 6

We can rewrite the equation as follows $(x +)(x +3) =0$

STEP 7

Now, we can solve for $x$ by setting each factor equal to zero and solving for $x$ .
$x +7 =0 \quad \text{and} \quad x +3 =0$

STEP 8

olving $x +7 =0$ for $x$ gives $x = -7$

STEP 9

olving $x +3 =$ for $x$ gives $x = -3$ So, the solutions to the equation $-2x^{2} -20x -42 =$ are $x = -7$ and $x = -3$ .

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