How do you solve $x^{2} + 2 x = 3$ $x^2 + 2x = 3$ by completing the square?

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How do you solve $x^{2} + 2 x = 3$ $x^2 + 2x = 3$ by completing the square?

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Answer 1 · 2017-03-26T19:17:06

Because the sign of the x term is positive, we use the pattern:
${(x + a)}^{2} = x^{2} + 2 a x + a^{2} [1]$ $(x+a)^2=x^2+2ax+a^2" [1]"$

Explanation:

Given: $x^{2} + 2 x = 3$ $x^2 + 2x = 3$

Add $a^{2}$ $a^2$ to both sides:

$x^{2} + 2 x + a^{2} = 3 + a^{2} [2]$ $x^2 + 2x + a^2= 3 + a^2" [2]"$

Please observe that the left side of equation [2] now resembles the right side of equation [1]. This means that we can set the middle term of equation [1] equal to the middle term of equation [2], to find the value of "a":

$2 a x = 2 x$ $2ax = 2x$

$a = 1$ $a = 1$

Substitute 1 for "a" in equation [2]:

$x^{2} + 2 x + 1^{2} = 3 + 1^{2} [3]$ $x^2 + 2x + 1^2= 3 + 1^2" [3]"$

Because we have completed the square, the left side of equation [3] collapses into a square with $a = 1$ $a =1$ and the right side becomes a single constant:

${(x + 1)}^{2} = 4 [4]$ $(x + 1)^2 = 4" [4]"$

Perform the square root operation on both sides:

$x + 1 = \pm 2 [5]$ $x + 1 = +-2" [5]"$

Subtract 1 from both sides:

$x = - 1 \pm 2 [6]$ $x = -1 +-2" [6]"$

$x = 1 and x = - 3$ $x = 1 and x = -3$

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How do you solve $x^{2} + 2 x = 3$ $x^2 + 2x = 3$ by completing the square?

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