How do you solve $5 x^{2} - 30 x + 5 = 0$ $5x^2-30x+5=0$ by completing the square?

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How do you solve $5 x^{2} - 30 x + 5 = 0$ $5x^2-30x+5=0$ by completing the square?

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Answer 1 · 2016-08-04T17:54:54

$x = 3 - 2 \sqrt{2}$ $x=3-2sqrt2$ or $x = 3 + 2 \sqrt{2}$ $x=3+2sqrt2$

Explanation:

To solve $5 x^{2} - 30 x + 5 = 0$ $5x^2-30x+5=0$ , let us first divide both sides by $5$ $5$ whic gives us

$x^{2} - 6 x + 1 = 0$ $x^2-6x+1=0$

Now to complete square for $x^{2} - 6 x$ $x^2-6x$ , recalling identity ${(x - a)}^{2} = x^{2} - 2 a x + a^{2}$ $(x-a)^2=x^2-2ax+a^2$ , we must add and subtract square of half of the coefficient of $x$ $x$ i.e. ${(\frac{6}{2})}^{2} = 9$ $(6/2)^2=9$ , hence we have

$x^{2} - 6 x + 9 - 9 + 1 = 0$ $x^2-6x+9-9+1=0$ or

${(x - 3)}^{2} - 8 = 0$ $(x-3)^2-8=0$ or ${(x - 3)}^{2} - {(2 \sqrt{2})}^{2} = 0$ $(x-3)^2-(2sqrt2)^2=0$ which can be factorized as

$(x - 3 + 2 \sqrt{2}) (x - 3 - 2 \sqrt{2}) = 0$ $(x-3+2sqrt2)(x-3-2sqrt2)=0$

Hence $x = 3 - 2 \sqrt{2}$ $x=3-2sqrt2$ or $x = 3 + 2 \sqrt{2}$ $x=3+2sqrt2$

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How do you solve $5 x^{2} - 30 x + 5 = 0$ $5x^2-30x+5=0$ by completing the square?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

How do you solve 5x2−30x+5=05x^2-30x+5=0 by completing the square?

1 Answer

Explanation:

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How do you solve $5 x^{2} - 30 x + 5 = 0$ $5x^2-30x+5=0$ by completing the square?