Question

Use the Quadratic Formula to solve the equation x^2 - 8x = -24

20 Points! Thanks!

Answer 1

Quadratic formula

`\boldsymbol{\sf{x^(2) -8x=-24 }}`

We move the expression to the left side and then change its sign.

`\boldsymbol{\sf{x^(2) -8x+24=0 } }`

We use the quadratic formula to solve the quadratic equation ax^2 + bx + c = 0

`\boldsymbol{\sf{x=(-(-8)\pm√((-8)^2+4\cdot1\cdot24 ) )/(2\cdot1) \ Simplify\:sign \ - \boldsymbol{\sf{x=(8\pm√((-8)^2+4\cdot1\cdot24 ) )/(2\cdot1) }} }}`

A negative number raised to the power of an even number is a positive number. So the negative sign is removed.

`\boldsymbol{\sf{x=\frac{8\pm\sqrt{ 8^(2)-4\cdot1\cdot24 } }{2\cdot1} \iff \ we \ simplify \ x=(8\pm√(-32) )/(2\cdot1) } }`

We organize the part that can be taken from the radical sign inside the square root.

`\boldsymbol{\sf{x=(8\pm4√(2i) )/(2) \to Separate \ answer \left \{ {{x=(8+4√(2i) )/(2) } \atop {x=(8-4√(2i) )/(2)}} \right. }}`

We reduce the fraction.

`\boldsymbol{\sf{x=4+2√(2i)}} \\ \\ \boldsymbol{\sf{x=(8-4√(2i) )/(2) }}`

We reduce the fraction.

`\boxed{\boldsymbol{\sf{\left \{ {{x=4+2√(2i) } \atop {x=4-2√(2i) }} \right. \to Answer }}}`

We change only the address: x=4+2i√2 or x=4-2-2i√2. LAST ALTERNATIVE