A number multiplied by itself is 5 more than 4 times the number. What is the number?

Question

Ethan Adkins · Accepted Answer

#x=-1 and x=+5#

Breaking the question down into its component parts.

A number #->................................................." "x# multiplied by itself #->....................................." "x^2# is #->............................................................." "x^2=?# 5 more than #->.............................................." "x^2=5+?# 4 times the number #->..................................." "x^2=5+4x# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Writing this as a quadratic we have:

#x^2-4x-5=0#

Note that #(+1)xx(-5)=-5 and 1-5=-4#

So we may factorise this as:

#(x+1)(x-5)=0#

#=>x=-1 and x=+5#

Savannah Anderson · Answer

undefined Let's denote the number as $ x $. According to the given information, we have the equation $ x^2 = 4x + 5 $. Rearranging this equation to set it equal to zero gives us $ x^2 - 4x - 5 = 0 $. This is a quadratic equation, and we can solve it using various methods like factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula: $ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} $, where $ a = 1 $, $ b = -4 $, and $ c = -5 $. Substituting these values into the formula, we get $ x = \frac{{-(-4) \pm \sqrt{{(-4)^2 - 4(1)(-5)}}}}{{2(1)}} $. This simplifies to $ x = \frac{{4 \pm \sqrt{{16 + 20}}}}{2} $, which further simplifies to $ x = \frac{{4 \pm \sqrt{36}}}{2} $. Hence, $ x = \frac{{4 \pm 6}}{2} $, giving us two solutions: $ x = \frac{{4 + 6}}{2} $ and $ x = \frac{{4 - 6}}{2} $. Therefore, the solutions are $ x = 5 $ and $ x = -1 $.