How do you solve $15=8x^2-14x$ ?

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Answer 1 · 2016-04-22T21:01:24

$color(blue)(color(green)( x = 7/8+-13/8) = 5/2 or 3/4)$

I am opting to use vertex form equation

Write as: $" "y=8x^2-14x-15$

Compare to standard form: $" "y=ax^2+bx+c$

Where $" "a=8"; "b=-14"; "c=-15$

Vertex form is: $" "y=a(x+b/(2a))^2 +c - a(b/(2a))^2$

$=>y=8(x-14/(2xx8))^2 -15-((-14)^2)/(4xx8)$

$=>y=8(x-7/8)^2 -169/8$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Vertex "->(x,y)=(+7/8,-169/8)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Set $y=0$ giving:

$169/64=(x-7/8)^2$

Taking the square root of both sides

$+-13/8 = x-7/8$

$color(blue)(=> x = 7/8+-13/8 = 5/2 or 3/4)$

Tony B Tony B

How do you solve 15=8x^2-14x15=8x^2-14x?