Quadratic Word Problems | MathHelp.com - By MathHelp.com
00:0-1 | A number is 56 less than its square . Find | |
00:03 | the number to solve this problem , let's translate the | |
00:08 | first sentence into an equation . A number that's X | |
00:14 | is equals 56 less than its square . That's X | |
00:19 | squared minus 56 . Remember that less than switches the | |
00:24 | order around . In other words , 56 less than | |
00:29 | its square is not 56 minus x squared it's X | |
00:34 | squared minus 56 . Next , since we have an | |
00:38 | X squared term in our equation , we set it | |
00:42 | equal to zero by subtracting X from both sides and | |
00:46 | we have zero equals x squared minus x minus 56 | |
00:53 | . Next we factor the right side as the product | |
00:56 | of two by no meals . In the first position | |
01:00 | of each binomial , we have the factors of X | |
01:03 | squared X and X in the second position of each | |
01:07 | by no meal . We're looking for the factors of | |
01:10 | negative 56 that add to negative one Which are negative | |
01:15 | eight and positive seven . So we have zero equals | |
01:20 | x minus eight times X plus seven , which means | |
01:24 | that either zero equals x minus eight or zero equals | |
01:28 | x plus seven . Finally , in the first equation | |
01:32 | , we add 8 to both sides to get eight | |
01:35 | equals x . And in the second equation we subtract | |
01:39 | seven from both sides to get -7 equals x . | |
01:44 | So eight equals X . Or negative seven equals X | |
01:48 | . It's important to understand that both of these answers | |
01:51 | work plugging in eight back into the original problem , | |
01:56 | We have eight is 56 less than eight squared or | |
02:01 | eight equals eight squared minus 56 which simplifies to eight | |
02:06 | equals 64 minus 56 or eight equals eight , which | |
02:11 | is a true statement . And plugging a negative seven | |
02:15 | back into the original problem , we have negative seven | |
02:19 | is 56 . Less than negative seven squared or negative | |
02:24 | seven equals negative seven squared minus 56 . Which simplifies | |
02:30 | to negative seven equals 49 -56 , or negative seven | |
02:36 | equals negative seven , which is also a true statement | |
00:0-1 | . |
DESCRIPTION:
A number is 56 less than its square. Find the number. To solve this problem, letâs translate the first sentence into an equation. A number, thatâs x, is, =, 56 less than itâs square, thatâs x squared â 56. Remember that âless thanâ switches the order around. In other words, â56 less than its squareâ is not 56 minus x squared, itâs x squared minus 56. Next, since we have an x squared term in our equation, we set it equal to 0 by subtracting x from both sides, and we have 0 = x squared â x â 56. Next, we factor the right side as the product of two binomials. In the first position of each binomial, we have the factors of x squared, x and x. In the second position of each binomial, weâre looking for the factors of -56 that add to -1, which are -8 and positive 7. So we have 0 = x - 8 times x + 7, which means that either 0 = x â 8 or 0 = x + 7. Finally, in the first equation, we add 8 to both sides, to get 8 = x. And in the second equation, we subtract 7 from both sides, to get -7 = x. So 8 = x or -7 = x. Itâs important to understand that both of these answers work. Plugging an 8 back into the original problem, we have 8 is 56 less than 8 squared, or 8 = 8 squared â 56, which simplifies to 8 = 64 â 56, or 8 = 8, which is a true statement. And plugging a -7 back into the original problem, we have -7 is 56 less than -7 squared, or -7 = -7 squared â 56, which simplifies to -7 = 49 â 56, or -7 = -7, which is also a true statement.
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