2.13 use square roots to solve quadratics example 1 solve quadratic equations solution write...
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2.13 Use Square Roots to Solve Quadratics
Example 1 Solve quadratic equationsSolve quadratic equations
Solution
Write original equation.
5___2 z 9
9
45 a. 2 z 47 b. 2 rSolve the equation.
45 a. 2 zAdd __ to each side.
____z Take sq root of each side.
Simplify.____z 3The solutions are ____ and ____.3 3
2.13 Use Square Roots to Solve Quadratics
Example 1 Solve quadratic equationsSolve quadratic equations
Solution
Write original equation.
7___2 r 3
45 a. 2 z 47 b. 2 rSolve the equation.
47 b. 2 rSubtract __ from each side.
Negative real numbers do not have real ____________.square roots
So, there is ____________.no solution
2.13 Use Square Roots to Solve Quadratics
Example 2 Take square root of a fractionTake square root of a fraction
SolutionWrite original equation.
25_______
2 k25
9
25
9
Solve the equation 25k 2 = 9.
925 2 k
Divide each side by ____.
__________
k Take sq root of each side.
Simplify._______
k5
3
The solutions are ____
and ____
.5
3
5
3
2.13 Use Square Roots to Solve QuadraticsCheckpoint. Solve the equation. Checkpoint. Solve the equation.
1083 .1 2 x3 3
2x 36x 36 6
1717 .2 2 t
2t 0t 0 0
17 17
2.13 Use Square Roots to Solve QuadraticsCheckpoint. Solve the equation. Checkpoint. Solve the equation.
418 .3 2 p81 81
2p81
4
p81
4
9
2
___2 x
2.13 Use Square Roots to Solve Quadratics
Example 3 Approximate solutions of a quadratic equationApproximate solutions of a quadratic equation
Solution
Write original equation.
3___4 2 x 205
2334 2 xSubtract __ from each side
Divide each side by ___.
Take sq roots of each side.____x 5
The solutions are ______ and _____.24.2 24.2
Solve 4x 2 + 3 = 23. Round the solution to the nearest hundredth.
4
Use a calculator. Round to the nearest hundredth.____x 24.2
2.13 Use Square Roots to Solve QuadraticsCheckpoint. Solve the equation. Round the solutions to Checkpoint. Solve the equation. Round the solutions to the nearest hundredth.the nearest hundredth.
2 22x 8x 8 83.2
972 .4 2 x
22x 167 7
2.13 Use Square Roots to Solve QuadraticsCheckpoint. Solve the equation. Round the solutions to Checkpoint. Solve the equation. Round the solutions to the nearest hundredth.the nearest hundredth.
6 62g 3g 3 .731
1916 .5 2 g
26g 181 1
_____ _______ are solutions The
____1x
2.13 Use Square Roots to Solve Quadratics
Example 4 Solve a quadratic equationSolve a quadratic equation
Solution
Write original equation.
___1 2 x 6
3015 2 xDivide each side by ___.
Take sq roots of each side.
_____x6
61 45.1
Solve 5(x + 1) 2 = 30. Round the solution to the nearest hundredth.
5
Subtract __ from each side61 1
_____. _______ and 61 45.3
1243 .6 2 m
2.13 Use Square Roots to Solve QuadraticsCheckpoint. Solve the equation. Round the solutions to Checkpoint. Solve the equation. Round the solutions to the nearest hundredth, if necessary.the nearest hundredth, if necessary.
3 3
4m 4
m 24
24m 4
4 4
m ,6 2
3234 .7 2 a
2.13 Use Square Roots to Solve QuadraticsCheckpoint. Solve the equation. Round the solutions to Checkpoint. Solve the equation. Round the solutions to the nearest hundredth, if necessary.the nearest hundredth, if necessary.
4 4
3a 8
a 83
23a 8
3 3
a ,83.5 17.0
2.13 Use Square Roots to Solve Quadratics
Pg. 129, 2.13 #1-23