Question

Which are the solutions of x2 = –13x – 4? 0, 13 0, –13 StartFraction 13 minus StartRoot 153 EndRoot Over 2 EndFraction comma StartFraction 13 + StartRoot 153 EndRoot Over 2 EndFraction StartFraction negative 13 minus StartRoot 153 EndRoot Over 2 EndFraction comma StartFraction negative 13 + StartRoot 153 EndRoot Over 2 EndFraction

Answer 1

Solution of the given expression  $x^2 = -13x-4$ is $x=\frac{-13+\sqrt{153}}{2}\,\,and\,\,x=\frac{-13-\sqrt{153}}{2}$

Correct options are: Start Fraction negative 13 minus Start Root 153 End Root Over 2 End Fraction comma Start Fraction negative 13 + Start Root 153 End Root

Step-by-step explanation:

We need to find solutions of $x^2 = -13x-4$

We need to solve the quadratic equation and find values of x.

Solving:

$x^2 = -13x-4$

Rearranging the terms:

$x^2+13x+4=0$

Solving the quadratic equation using quadratic formula:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

where a = 1, b= 13 and c=4

putting values:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(13)\pm\sqrt{(13)^2-4(1)(4)}}{2(1)}\\x=\frac{-13\pm\sqrt{169-16}}{2}\\x=\frac{-13\pm\sqrt{153}}{2}\\x=\frac{-13+\sqrt{153}}{2}\,\,and\,\,x=\frac{-13-\sqrt{153}}{2}$

So, Solution of the given expression  $x^2 = -13x-4$ is $x=\frac{-13+\sqrt{153}}{2}\,\,and\,\,x=\frac{-13-\sqrt{153}}{2}$

Correct options are: Start Fraction negative 13 minus Start Root 153 End Root Over 2 End Fraction comma Start Fraction negative 13 + Start Root 153 End Root

Keywords: Solving Quadratic Equations

Learn more about Solving Quadratic Equations at:

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Answer 2

Answer:

$x_{1}=\frac{-13+\sqrt{153}}{2}\\x_{2}=\frac{-13-\sqrt{153}}{2}$

Step-by-step explanation:

The given expression is

$x^{2}=-13x-4$

To solve this quadratic equation, we first need to place all terms in one side of the equation sign

$x^{2} +13x+4=0$

Now, to find all solutions of this expression, we have to use the quadratic formula

$x_{1,2}=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}$

Where $a=1$, $b=13$ and $c=4$

Replacing these values in the formula, we have

$x_{1,2}=\frac{-13\±\sqrt{(13)^{2}-4(1)(4)}}{2(1)}\\x_{1,2}=\frac{-13\±\sqrt{169-16}}{2}=\frac{-13\±\sqrt{153}}{2}$

So, the solutions are

$x_{1}=\frac{-13+\sqrt{153}}{2}\\x_{2}=\frac{-13-\sqrt{153}}{2}$

If we approximate each solution, it would be

$x_{1}=\frac{-13+\sqrt{153}}{2}\approx -0.32\\\\x_{2}=\frac{-13-\sqrt{153}}{2} \approx -12.68$