Question

HELP WILL GIVE 40 POINTS AND BRAINLIEST!!!! Solve these two (second-degree) quadratic equations by factoring. $2x^{2}+6x=0$ & $x^{2}+9x+14=0$

Answer 1

Answer:

Step-by-step explanation:

First equation:  2x^2 + 6x = 0 factors into 2x(x + 3) = 0, so either x = 0 or x = -3.

Second equation:  x^2 + 9x + 14 = 0 factors into (x + 2)(x + 7) = 0.  Thus, either x = -2 or x = -7

Answer 2

Hi there! Hopefully this helps!

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Answer for $2x^{2} + 6x = 0$:

x = 0

x = -3

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|$2x^{2} + 6x = 0$

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|First we factor out x

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$x(2x+6)=0$

To find equation solutions, solve $x = 0$ and $2x+6 = 0$

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$x = 0$

$x = -3$

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Answer for $x^{2}+ 9x + 14 = 0$:

x = -2

x = -7

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|$x^{2}+ 9x + 14 = 0$

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|To solve the equation, factor $x^{2}+ 9x + 14$ using formula $x^{2} + (a + b)x + ab = (x+a) (x+b).$ To find $a$ and $b$, set up a system to be solved.

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$a + b = 9$

$ab = 14$

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Since $ab$ is positive, $a$ and $b$ have the same sign. Since $a + b$ is positive, $a$ and $b$ are both positive. List all such integer pairs that give product 14.

1, 14

2, 7

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Calculate the sum for each pair.

1 + 14 = 15

2 + 7 = 9

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The solution is the pair that gives sum 9.

$a = 2$

$b = 7$.

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Rewrite factored expression $(x+a)(x+b)$ using the obtained values.

$(x+2)(x+7)$

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To find equation solutions, solve $x + 2 = 0$ and $x + 7 = 0$.

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$x = -2$

$x = -7$