Question

Use the quadratic formula to find the solutions to the quadratic equation below x^2-6x-5=0

Answer 1

The quadratic equation
`x^2` -6x-5=0 is solved using the quadratic formula to find its solutions, giving the answers x = 3 +
`√(14)` and x = 3 -
`√(14)`.

Step-by-step explanation:

To solve the quadratic equation
`x^2` -6x-5=0 using the quadratic formula, we first identify the coefficients a, b, and c from the general form a
`x^2`+bx+c=0. In this case, a=1, b=-6, and c=-5. The quadratic formula is:

x = (-b ±
`√((b^2 - 4ac)) / (2a))`

Plugging these values into the formula gives us:

`x = (-(-6) ± √(((-6)^2 - 4(1)(-5))) / (2(1))) \\x = (6 ± √((36 + 20)) / 2) \\x = (6 ± √((56)) / 2) \\x = (6 ± √((4*14)) / 2) \\x = (6 ± 2√(14) ) / 2\\x = 3 ± √(14)`

Therefore, the solutions for the quadratic equation are x = 3 +
`√(14)` and x = 3 -
`√(14)`.

Answer 2

`\large\boxed{x=3-√(14)\ \vee\ x=3+√(14)}`

Step-by-step explanation:

`x^2-6x-5=0\qquad\text{add 5 to both sides}\\\\x^2-6x=5\\\\x^2-2(x)(3)=5\qquad\text{add}\ 3^2\ \text{to both sides}\\\\x^2-2(x)(3)+3^2=5+3^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-3)^2=5+9\\\\(x-3)^2=14\to x-3=\pm√(14)\qquad\text{add 3 to both sides}\\\\x=3-√(14)\ \vee\ x=3+√(14)`