SOLUTION: [ solve this quadratic equation using the quadratic formula: x^2-22x+21=0 ]

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: [ solve this quadratic equation using the quadratic formula: x^2-22x+21=0 ]      Log On


   



Question 818675: [ solve this quadratic equation using the quadratic formula: x^2-22x+21=0 ]
Found 2 solutions by TimothyLamb, jim_thompson5910:
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 - 22x + 21 = 0
---
the above quadratic equation is in standard form, with a=1, b=-22, and c=21
---
to solve the quadratic equation, by using the quadratic formula, plug this:
1 -22 21
into this: https://sooeet.com/math/quadratic-equation-solver.php
---
the two real roots (i.e. the two solutions), of the quadratic equation are:
x = 21
x = 1
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
---
Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-22x%2B21=0 Start with the given equation.


Notice that the quadratic x%5E2-22x%2B21 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-22, and C=21


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-22%29+%2B-+sqrt%28+%28-22%29%5E2-4%281%29%2821%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-22, and C=21


x+=+%2822+%2B-+sqrt%28+%28-22%29%5E2-4%281%29%2821%29+%29%29%2F%282%281%29%29 Negate -22 to get 22.


x+=+%2822+%2B-+sqrt%28+484-4%281%29%2821%29+%29%29%2F%282%281%29%29 Square -22 to get 484.


x+=+%2822+%2B-+sqrt%28+484-84+%29%29%2F%282%281%29%29 Multiply 4%281%29%2821%29 to get 84


x+=+%2822+%2B-+sqrt%28+400+%29%29%2F%282%281%29%29 Subtract 84 from 484 to get 400


x+=+%2822+%2B-+sqrt%28+400+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2822+%2B-+20%29%2F%282%29 Take the square root of 400 to get 20.


x+=+%2822+%2B+20%29%2F%282%29 or x+=+%2822+-+20%29%2F%282%29 Break up the expression.


x+=+%2842%29%2F%282%29 or x+=++%282%29%2F%282%29 Combine like terms.


x+=+21 or x+=+1 Simplify.


So the solutions are x+=+21 or x+=+1