Question

What are the solutions of this quadratic equation?

x² + 4 = 8x + 5

A = 4 ± √7
B = 4 ± √17
C = 8 ± √34
D = 82√17

Answer 1

Given equation to us is
`x^2+4=8x+5`

And we need to find out the solutions to the given equation. We can rewrite the equation as ,

`\longrightarrow x^2+4-8x-5=0`

Simplify,

`\longrightarrow x^2-8x-1=0`

Now this equation is in standard form of quadratic equation which is
`ax^2+bx+c=0`

With respect to the standard form ,

• 
  `a =1`
• 
  `b =-8`
• 
  `c =-1`

Now we may use the quadratic formula for finding the roots as ,

Quadratic formula:-

`\longrightarrow x =(-b\pm√(b^2-4ac))/(2a)\\`

So that,

`\longrightarrow x =(-(-8)\pm√(-8^2-4(1)(-1)))/(2(1))\\`

`\longrightarrow x =(8\pm√(64+4))/(2)\\`

`\longrightarrow x =(8\pm √(68))/(2)\\`

`\longrightarrow x =(8\pm 2√(17))/(2)\\`

`\longrightarrow\underline{\underline{ x = 4\pm √(17)}}`

And we are done!