guringpw
2021-12-15
Answered

What are the roots of the equation ${x}^{2}-5x+1=0$ ?

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lalilulelo2k3eq

Answered 2021-12-16
Author has **38** answers

You can solve this equation using 2 methods, one being completing the square method, and the other by using the quadratic formula.

1) Commencing completing the square method,

${x}^{2}-5x+1=0$

Subtract 1 on both sides,

${x}^{2}-5x=-1$

Add 6.25 on both sides,

${x}^{2}-5x+6.25=-1+6.25$

Apply perfect quadratic square formula,

${(x-2.5)}^{2}=5.25$

Square root both sides,

$x-2.5=\pm \sqrt{5.25}$

Add 2.5 to both sides,

$x=\pm \sqrt{5.25}+2.5$

Hence,

$x=4.79128784$ or $0.20871215$

2) Commencing quadratic formula method,

${x}^{2}-5x+1=0$

Quadratic equation,

$a{x}^{2}+bx+c=0$

Substitute$a=1,b=-5,c=1$ into the quadratic formula.

$x=\frac{5\pm \sqrt{21}}{2}$

Hence,

$x=4.79128784$ or $0.20871215$

1) Commencing completing the square method,

Subtract 1 on both sides,

Add 6.25 on both sides,

Apply perfect quadratic square formula,

Square root both sides,

Add 2.5 to both sides,

Hence,

2) Commencing quadratic formula method,

Quadratic equation,

Substitute

Hence,

censoratojk

Answered 2021-12-17
Author has **46** answers

Find the roots:

${x}^{2}-5x+1=0\Rightarrow$ quadratic equation

The standard form for a quadratic equation is$a{x}^{2}+bx+c=0$ , where $a=1,b=-5$ and $c=1$ . Note: $a\ne 0$

Solve this quadratic equation using the quadratic formula:

$x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$

Substitute the known values into the formula.

$x=\frac{-(-5)\pm \sqrt{{(-5)}^{2}-4\cdot 1\cdot 1}}{2\cdot 1}$

Simplify.

$x=\frac{5\pm \sqrt{25-4}}{2}$

Simplify.

$x=\frac{5\pm \sqrt{21}}{2}$

Solutions for x. roots

$x=\frac{5+\sqrt{21}}{2},\frac{5-\sqrt{21}}{2}$

The standard form for a quadratic equation is

Solve this quadratic equation using the quadratic formula:

Substitute the known values into the formula.

Simplify.

Simplify.

Solutions for x. roots

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