How do you solve using the completing the square method $x^2 + 6x = 7$ ?

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Answer 1 · 2017-07-20T16:02:28

$x=1 or -7$

$x^2+6x=7$

half the coefficient of $x$ and square it

$6rarr3^2$

add and subtract this value

$color(red)(x^2+6x+3^2)-3^2=7$

$color(white)(==)uarr$ the terms in red form a perfect square

$color(red)((x^2+6x+3^2))-9=7$

$color(white)(==)darr$

$=>color(red)((x+3)^2)=7+9$

$(x+3)^2=16$

now solve for $x$

$=>x+3=+-sqrt16$

$x+3=+-4$

$x=-3+-4$

$x=1 or -7$

How do you solve using the completing the square method x^2 + 6x = 7x^2 + 6x = 7?