Question

Solve using the quadratic formula x^2 - 6x +32 = 7 or

Answer 1

hi the answers are x =(6-√164)/2=3-√ 41 = -3.403
x =(6+√164)/2=3+√ 41 = 9.403

Answer 2

The general form of a quadratic equation is expressed as

ax^2 + bx + c

The given equation is

x^2 - 6x + 32 = 7

x^2 - 6x + 32 - 7 = 0

x^2 - 6x + 25 = 0

By comparing with the given equation,

a = 1, b = - 6, c = 25

We would solve the equation by applying the quadratic formula which is expressed as

`x\text{ = }\frac{-b+-\sqrt[]{b^2-4ac}}{2a}`

We would substitute the given values into the equation. It becomes

`\begin{gathered} x\text{ = }\frac{-\text{ - 6 +-}\sqrt[]{-6^2-4(1*25)}}{2\text{ }*1} \\ x\text{ = }\frac{6+-\sqrt[]{36-100}_{}_{}}{2} \\ x\text{ = }\frac{6\text{ +-}\sqrt[]{-64}}{2} \end{gathered}`

Recall that the root of a negative number is a complex root. It would be written in form of complex numbers. It becomes

`\begin{gathered} x\text{ = }\frac{6\text{ +-8i}}{2} \\ x\text{ = }\frac{6\text{ + 8i}}{2}\text{ or x = }\frac{6\text{ - 8i}}{2} \\ x\text{ = 3 + 4i or x = 3 - 4i} \end{gathered}`