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Volgvan
2 years ago
10

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

rtFraction 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
Mathematics
2 answers:
klasskru [66]2 years ago
5 0

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:

  • brainly.com/question/4460262
  • brainly.com/question/7361044
  • brainly.com/question/1414350

#learnwithBrainly

Svetradugi [14.3K]2 years ago
3 0

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

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