How do you solve the equation $x^{2} + 4 x = 6$ $x^2+4x=6$ by completing the square?

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How do you solve the equation $x^{2} + 4 x = 6$ $x^2+4x=6$ by completing the square?

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Answer 1 · 2017-02-27T19:30:00

$x = - 2 \pm \sqrt{10}$ $x=-2+-sqrt(10)$

Explanation:

First subtract $6$ $6$ from both sides to get the quadratic equation into standard form:

$x^{2} + 4 x - 6 = 0$ $x^2+4x-6 = 0$

The difference of squares identity can be written:

$a^{2} - b^{2} = (a - b) (a + b)$ $a^2-b^2 = (a-b)(a+b)$

Use this with $a = x + 2$ $a=x+2$ and $b = \sqrt{10}$ $b=sqrt(10)$ as follows:

$0 = x^{2} + 4 x - 6$ $0 = x^2+4x-6$

$0 = x^{2} + 4 x + 4 - 10$ $color(white)(0) = x^2+4x+4-10$

$0 = {(x + 2)}^{2} - {(\sqrt{10})}^{2}$ $color(white)(0) = (x+2)^2-(sqrt(10))^2$

$0 = ((x + 2) - \sqrt{10}) ((x + 2) + \sqrt{10})$ $color(white)(0) = ((x+2)-sqrt(10))((x+2)+sqrt(10))$

$0 = (x + 2 - \sqrt{10}) (x + 2 + \sqrt{10})$ $color(white)(0) = (x+2-sqrt(10))(x+2+sqrt(10))$

Hence:

$x = - 2 \pm \sqrt{10}$ $x = -2+-sqrt(10)$

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How do you solve the equation $x^{2} + 4 x = 6$ $x^2+4x=6$ by completing the square?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you solve the equation x2+4x=6x^2+4x=6 by completing the square?

1 Answer

Explanation:

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Impact of this question

How do you solve the equation $x^{2} + 4 x = 6$ $x^2+4x=6$ by completing the square?