Summary: Algebra

Read the summary and the most important questions on algebra

• Algebra

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• Solve x2 = −100 by using square roots.

  There are no real solutions.
  There is no real number whose square is negative. Therefore, there are no real solutions.

• Solve the equation m2 − 350 = 11 by using square roots.

  19
   m2 − 350 = 11
  m2 = 361 Add 350 to both sides.
  m = Take the square root of both sides.
  m = ±19

• Solve x2 − 10 = 0. If necessary, round to the nearest hundredth.

  3.16
   x2 − 10 = 0
  x2 = 10 Add 10 to both sides.
  x = Take the square root of both sides.
  x = ±3.16

• Solve the equation 64x2 − 144 = −23 by using square roots.

  11/8
   64x2 − 144 = −23
  64x2 = 121 Add 144 to both sides.
  x2 = 121/64 Divide both sides by 64.
  x = Take the square root of both sides.
  x = ±11/8

• Sam wants to build a wooden deck on his patio, which is in the shape of a parallelogram. The area of the patio is 280 ft2. Find the base. Round your answer to the nearest foot.Hint : Use A = bh.

  18
   A = bh Use the formula for the area of a parallelogram.
  280 = (5x)(6x) Substitute.
  280 = 30x2 Simplify.
  28/3 = x2 Divide both sides by 30 and simplify.
  x = Take the square root of both sides.
  x ≈ 3 Length cannot be negative.
  The width is 6x ≈ 18 ft.

• Use the graph of the related function to identify the solution(s) of the equation 9x2 + 36 = 36x.

  x=2
   9x2 + 36 = 36x
  Find the zeros.
  The zero is 2.

• Use the graph of the related function to identify the solution(s) of the equation x2 = 6x − 10.

  no real aanswers
  
  x2 = 6x − 10
  Find the zeros.There are no real zeros.

• Solve the equation x2 − 6x + 5 = 0 by graphing the related function.

  1 and 5
   
  x2 − 6x + 5 = 0Step 1 Write the related function.
  x2 − 6x + 5 = 0
  y = x2 − 6x + 5
  Step 2 Graph the function.
  
  Use a graphing calculator.
  Step 3 Find the zeros.
  
  The zeros are 1 and 5.

• Solve the quadratic equation x2 + 30x + 225 = 0 by factoring.

  x= -15

• Solve the quadratic equation x2 + 18x + 77 = 0 by factoring.

  x = −7; x = −11