How do you solve the equation $x^2+1.4x+0.49=0.81$ by completing the square?

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Answer 1 · 2016-12-18T09:28:47

$x = 0.2" "$ or $" "x = -1.6$

We will use the difference of squares identity, which can be written:

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

Given:

$x^2+1.4x+0.49 = 0.81$

Both the left hand and right hand side of this equation are perfect squares already:

$(x+0.7^2) = x^2+1.4x+0.49 = 0.81 = 0.9^2$

Hence:

$0 = (x+0.7^2)-0.9^2$

$color(white)(0) = ((x+0.7)-0.9)((x+0.7)+0.9)$

$color(white)(0) = (x-0.2)(x+1.6)$

Hence:

$x = 0.2" "$ or $" "x = -1.6$

How do you solve the equation x^2+1.4x+0.49=0.81x^2+1.4x+0.49=0.81 by completing the square?