How do you write #2x^2 - 10 + 3x = (x - 2)^2 + 1# in standard form?
1 Answer
May 14, 2016
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)|)))#
