How do you write #2x^2 - 10 + 3x = (x - 2)^2 + 1# in standard form?

1 Answer
May 14, 2016

#x^2+7x-15=0#

Explanation:

Recall that the general equation of a quadratic in standard form is:

#color(blue)(|bar(ul(color(white)(a/a)ax^2+bx+c=0color(white)(a/a)|)))#

In order to rewrite the given equation in standard form, you need to expand and collect like terms.

Given,

#2x^2-10+3x=(x-2)^2+1#

Expand and simplify the right side.

#2x^2-10+3x=color(darkorange)((x-2)(x-2))+1#

#2x^2-10+3x=color(darkorange)(x^2-4x+4)+1#

#2x^2-10+3x=x^2-4x+5#

Move all terms to the left side of the equation.

#2x^2color(white)(i)color(purple)(-x^2)+3xcolor(white)(i)color(purple)(+4x)-10color(white)(i)color(purple)(-5)=0#

Simplify.

#color(green)(|bar(ul(color(white)(a/a)color(black)(x^2+7x-15=0)color(white)(a/a)|)))#