Question 1

Solve the quadratic equation using the quadratic formula. Simplify your answer.x² + 4x = -5

Solve the quadratic equation using the quadratic formula. Simplify your answer.x² + 4x-example-1

Question 2

Solution

- The solution steps are given below:

$\begin{gathered} \text{ Given the quadratic equation:} \\ ax^2+bx+c=0 \\ \text{ The qudartic formula for finding the variable }x\text{ is:} \\ x=(-b\pm√(b^2-4ac))/(2a) \\ \\ \text{ Thus, we can solve the question given to us using the above formula} \\ x^2+4x=-5 \\ \text{ Rewrite the equation} \\ x^2+4x+5=0 \\ \therefore a=1,b=4,c=5 \\ \\ x=(-4\pm√(4^2-4(1)(5)))/(2(1)) \\ \\ x=(-4\pm√(16-20))/(2) \\ \\ x=(-4\pm√(-4))/(2)=(-4\pm√(4*-1))/(2) \\ \\ \text{ By the law of surds we have that:} \\ √(4*-1)=√(4)*√(-1) \\ \\ x=(-4\pm(√(4)*√(-1)))/(2) \\ \\ x=(-4\pm(2*√(-1)))/(2) \\ \\ x=-(4)/(2)\pm(2√(-1))/(2) \\ \\ x=-2\pm√(-1) \\ \\ \text{ But we know that }√(-1)=i \\ \\ \therefore x=-2\pm i \end{gathered}$

Final Answer

$x=-2\pm i$

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