Solve for x over the real numbers:x = -2. x^2 - 8 x + 6
Hint: | Rewrite the right hand side of the equation.-2. x^2 - 8 x + 6 = -2 x^2 - 8 x + 6:x = -2 x^2 - 8 x + 6
Hint: | Move everything to the left hand side.Subtract -2 x^2 - 8 x + 6 from both sides:2 x^2 + 9 x - 6 = 0
Hint: | Write the quadratic equation in standard form.Divide both sides by 2:x^2 + (9 x)/2 - 3 = 0
Hint: | Solve the quadratic equation by completing the square.Add 3 to both sides:x^2 + (9 x)/2 = 3
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.Add 81/16 to both sides:x^2 + (9 x)/2 + 81/16 = 129/16
Hint: | Factor the left hand side.Write the left hand side as a square:(x + 9/4)^2 = 129/16
Hint: | Eliminate the exponent on the left hand side.Take the square root of both sides:x + 9/4 = sqrt(129)/4 or x + 9/4 = -sqrt(129)/4
Hint: | Look at the first equation: Solve for x.Subtract 9/4 from both sides:x = sqrt(129)/4 - 9/4 or x + 9/4 = -sqrt(129)/4
Hint: | Look at the second equation: Solve for x.Subtract 9/4 from both sides:Answer: x = sqrt(129)/4 - 9/4 or x = -9/4 - sqrt(129)/4
Lets x = Mary's age
Emily is there years older than twice her sister Mary's age = 2x + 3
Sum of both is less than 30:
x + 2x + 3 < 30
Solve for x
3x + 3 < 30
3x < 27
x < 9
Mary's age = 9
Inequality represents Mary's possible age:
0 < x < 9
Answer is the second one
0 < x < 9
You would have to mail it off
to fulfill manifest destiny, the American dream to expand, as well as reach the ocean on the west in order to have more options for trade
It is three hundred fifty-six thousandths.
