SOLUTION: 1. Solve by completing the square. x^2 – 4x + 4 = 0 2. Solve by completing the square. x^2 = 5x + 2 3. Solve by using the quadratic formula. x^2 = –3x + 8 4. Solve by

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1. Solve by completing the square. x^2 – 4x + 4 = 0 2. Solve by completing the square. x^2 = 5x + 2 3. Solve by using the quadratic formula. x^2 = –3x + 8 4. Solve by       Log On


   

Question 109283: 1. Solve by completing the square.
x^2 – 4x + 4 = 0
2. Solve by completing the square.
x^2 = 5x + 2
3. Solve by using the quadratic formula. x^2 = –3x + 8
4. Solve by using the quadratic formula. 3x2 = 11x + 4
5. Solve. (x + 1)2 = 3
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1. Solve by completing the square.

x%5E2+%96+4x+%2B+4+=+0.......-4x write as -2x+-+2x, then group first two terms and second two terms
x%5E2+%2B+2x+-+2x+%2B+4+=+0.......

(x%5E2+%96+2x) - (2x+-+4) = 0.......factor out in first group x, and in second group 2
x(x – 2) - 2(x - 2) = 0.......factor out x-2
(x – 2)(x - 2) = 0.......solution


2. Solve by completing the square.

x%5E2+=+5x+%2B+2
write this first in standard form:
x%5E2+-+5x+-+2+=+0
coefitients are: a+=+1, b+=+-5, and c+=+-2
now apply the quadratic formula:
x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29
x%5B1%2C2%5D=%285+%2B-+sqrt+%28%28-5%29%5E2+-4%2A1%2A%28-2%29+%29%29+%2F+%282%2A1%29
x%5B1%2C2%5D=%285+%2B-+sqrt+%2825+%2B+8+%29%29+%2F+2
x%5B1%2C2%5D=%285+%2B-+sqrt+%2833%29%29+%2F+2
x%5B1%2C2%5D=%285+%2B-+5.74%29+%2F+2

x%5B1%5D=%285+%2B+5.74%29+%2F+2
x%5B1%5D=5.37+

x%5B2%5D=%285+-+5.74%29+%2F+2
x%5B2%5D=-0.74+%2F+2
x%5B2%5D=+-0.37


3. Solve by using the quadratic formula.
x%5E2+= –3x+%2B+8+
x%5E2+%2B+3x+-+8+=+0
coefitients are: a+=+1, b+=+3, and c+=+-8
now apply the quadratic formula:
x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29
x%5B1%2C2%5D=%28-3+%2B-+sqrt+%28%283%29%5E2+-4%2A1%2A%28-8%29+%29%29+%2F+%282%2A1%29
x%5B1%2C2%5D=%28-3+%2B-+sqrt+%289+%2B+32+%29%29+%2F+2
x%5B1%2C2%5D=%28-3+%2B-+sqrt+%2841%29+%29+%2F+2
x%5B1%2C2%5D=%28-3+%2B-+6.4%29+%2F+2

x%5B1%5D=%28-3+%2B+6.4%29+%2F+2
x%5B1%5D=+3.4+%2F+2
x%5B1%5D=+1.7

x%5B2%5D=%28-3+-+6.4%29+%2F+2
x%5B2%5D=%28+-+9.4%29+%2F+2
x%5B2%5D=%28+-4.7%29+%2F+2


4. Solve by using the quadratic formula.
3x%5E2+=+11x+%2B+4
3x%5E2+-+11x+-+4+=+0
coefitients are: a+=+3, b+=+-11, and c+=+-4
now apply the quadratic formula:
x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29
x%5B1%2C2%5D=%28-11+%2B-+sqrt+%28%28-11%29%5E2+-4%2A3%2A%28-4%29+%29%29+%2F+%282%2A3%29

x%5B1%2C2%5D=%28-11+%2B-+sqrt+%28121+%2B+48+%29%29+%2F+6
x%5B1%2C2%5D=%28-11+%2B-+sqrt+%28169+%29%29+%2F+6
x%5B1%2C2%5D=%28-11+%2B-+13%29+%2F+6

x%5B1%5D=%28-11+%2B+13%29+%2F+6
x%5B1%5D=+2+%2F+6
x%5B1%5D=+1+%2F+3

x%5B2%5D=%28-11+-+13%29+%2F+6
x%5B2%5D=+-+24+%2F+6
x%5B2%5D=+-+4+


5. Solve. %28x+%2B+1%292+=+3....divide both sides by 2
x%2B1+=+3%2F2...move 1 to the right
x+=+3%2F2+-+1....1=2%2F2, so
x+=+3%2F2+-+2%2F2
x+=+1%2F2