How do you solve h^2+48=16hh2+48=16h?

2 Answers
Mar 17, 2018

See a solution process below:

Explanation:

First, subtract color(red)(16h)16h from each side of the equation to put the equation in standard quadratic form:

h^2 - color(red)(16h) + 48 = 16h - color(red)(16h)h216h+48=16h16h

h^2 - 16h + 48 = 0h216h+48=0

Now, we can use the quadratic equation to solve this problem:

The quadratic formula states:

For color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0ax2+bx+c=0, the values of xx which are the solutions to the equation are given by:

x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))x=b±b2(4ac)2a

Substituting:

color(red)(1)1 for color(red)(a)a

color(blue)(-16)16 for color(blue)(b)b

color(green)(48)48 for color(green)(c)c gives:

h = (-color(blue)(-16) +- sqrt(color(blue)(-16)^2 - (4 * color(red)(1) * color(green)(48))))/(2 * color(red)(1))h=16±162(4148)21

h = (16 +- sqrt(256 - 192))/2h=16±2561922

h = (16 +- sqrt(64))/2h=16±642

h = (16 - 8)/2h=1682 and h = (16 + 8)/2h=16+82

h = 8/2h=82 and h = 24/2h=242

h = 4h=4 and h = 12h=12

The Solution Set Is: h = {4, 12}h={4,12}

Another method is to factor the quadratic as:

(h - 12)(h - 4) = 0(h12)(h4)=0

The solve each term on the left for 00:

Solution 1:

h - 12 = 0h12=0

h - 12 + color(red)(12) = 0 + color(red)(12)h12+12=0+12

h - 0 = 12h0=12

h = 12h=12

Solution 2:

h - 4 = 0h4=0

h - 4 + color(red)(4) = 0 + color(red)(4)h4+4=0+4

h - 0 = 4h0=4

h = 4h=4

The Solution Set Is: h = {4, 12}h={4,12}

Mar 17, 2018

h=4" or "h=12h=4 or h=12

Explanation:

"rearrange equation into "color(blue)"standard form"rearrange equation into standard form

rArrh^2-16h+48=0larrcolor(blue)"in standard form"h216h+48=0in standard form

"the factors of + 48 which sum to - 16 are - 12 and - 4"the factors of + 48 which sum to - 16 are - 12 and - 4

rArr(h-12)(h-4)=0(h12)(h4)=0

"equate each factor to zero and solve for h"equate each factor to zero and solve for h

h-12=0rArrh=12h12=0h=12

h-4=0rArrh=4h4=0h=4

rArrh=12" or "h=4" are the solutions"h=12 or h=4 are the solutions