Question

4. Solve the quadratic by completing the square. 4x² + 16x +49 = 8

Answer 1

values of x are $x=\frac{5i}{2}-2\,\,and\,\,x=\frac{-5i}{2}-2$

Step-by-step explanation:

We need to solve the equation $4x^2+16x +49 = 8$ by completing square.

Solving:

$4x^2+16x +49 = 8\\4x² + 16x +49-8 = 0\\4x² + 16x +41 = 0$

We need to make the completing square form: $(a)^2+2(a)(b)+(b)^2=(a+b)^2$

$4x^2 + 16x +41 = 0\\Adding\,\,and\,\,subtracting\,\, 16 \\(2x)^2+2(2x)(4)+(4)^2+41-16=0\\(2x+4)^2+25=0\\(2x+4)^2=-25$

Finding value of x:

$(2x+4)^2=-25\\Taking\,\,square\,\,root\,\,on\,\,both\,\,sides:\\\sqrt{(2x+4)^2}=\sqrt{-25}\\ 2x+4=\pm5i\\so, 2x+4=5i\,\,and\,\,2x+4=-5i\\2x=5i-4\,\,and\,\,2x=-5i-4\\x=\frac{5i-4}{2} \,\,and\,\,x=\frac{-5i-4}{2} \\x=\frac{5i}{2}-2\,\,and\,\,x=\frac{-5i}{2}-2$

So, values of x are $x=\frac{5i}{2}-2\,\,and\,\,x=\frac{-5i}{2}-2$

Keywords: Solve Quadratic Equation

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