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Module 16

QuestionAnswer
Use the square root property to solve x^2=9 x^2=9 . Square root both sides. √x^2=±√9. x=±3
Solve 5x^2-50=0 add 50 to both sides (5x^2=50) Divide 5 from both sides (x^2=10) Square root both sides √x^2=±√10 Since there are no perfect squares within 10, you leave the problem as x=±√10
Solve for x using the square root property:(x+1)^2=12 square root both sides (√x+1)^2=±√12) (x+1=±√12) factor a perfect square out of 12 (x+1=±√4√3) x+1=±2√3 Subtract one from both sides x=-1±2√3
Solve y^2+6y=-8 First, divide the coefficient of y^2 (which is 6). (6/2)=3. Then add the square of the coefficient to both sides (3^2=9). y^2+6y+9=-8+9 this becomes y^2+6y+9=1 Factor y+3^2=1 square root both sides (√y+3)^2=±√1 y+3=1 solve for y (y=-2)
Complete the square: x^2+2x-5=0 Add 5 to both sides x^2+2x=5 Find the coefficient of x^2 (1/2(2)=1) Add the square of the coefficient to both sides (1^2=1) x^2+2x+1=5+1 turns into x^2+2x+1=6 Factor x+1^2=6 take the square root of both sides (√x+1)^2=±√6 x+1=±√6 subtract 1 x=±√6
Solve: 3p^2+36=0 Subtract 36 from both sides 3p^2=-36 divide each side by 3 p^2=-12 square root both sides √p^2=±√-12 becomes p=±√-12 p=i√12 factor out a perfect square p=i√4√3 solve for p: p=2i√3
Find the rate at which $3000 compounded annually grows to $4320 in 2 yrs : 4320=3000(1+r)^2 Divide 3000 from both sides (4320/3000)=3000/3000(1+r)^2 simplify 36/25=(1+r)^2 square root both sides ±√36/25=√(1+r)^2 turns into 6/5=1+r convert 1 into a fraction with a common denominator then subtract 6/5-5/5=r solve 1/5=r or 20%
Solve for r:16224=15000(1+r)^2 Divide 15000 from both sides (16224/15000=15000(1+r)^2 simplify 676/625=(1+r)^2 square root both sides ±√676/625=√(r+1)^2 (26/25=1+r) convert one into a fraction with a common denominator and subtract 26/25-25/25=r (1/25=r or 4%)
Find r: 882=800(1+r)^2 Divide 800 on both sides 882/800=800/800(1+r)^2 simplify 441/400=(1+r)^2 square root both sides ±√441/400=√(1+r)^2 21/20=1+r convert one into a fraction with a common denominator and subtract 21/20-20/20=r solve:1/20=r or 5%
solve for x: x^2=49 square root both sides and solve √x^2=±√49 x=±7