Answer: To solve -x²-2x=0 by factoring, we can factor out x from the left-hand side:
x(-x-2) = 0
This equation is true if either x = 0 or -x-2 = 0. Solving for x in the second equation:
-x-2 = 0
-x = 2
x = -2
Therefore, the solutions to the equation -x²-2x=0 are x = 0 and x = -2.
To solve x²-4x-8--6x by factoring, we can simplify it first by combining like terms:
x²-10x-8 = 0
To factor this quadratic, we need to find two numbers that multiply to -8 and add to -10. These numbers are -2 and -8, so we can write:
x²-2x-8x-8 = 0
(x²-2x) - (8x+8) = 0
x(x-2) - 8(x+1) = 0
(x-8)(x-2) = 0
Therefore, the solutions to the equation x²-4x-8--6x are x = 8 and x = 2.
To solve 3x² +12=-21x-24 by completing the square, we first need to move all the terms to one side:
3x² + 21x + 36 = 0
Next, we divide both sides by 3 to simplify the coefficient of x²:
x² + 7x + 12 = 0
To complete the square, we need to add and subtract (7/2)² = 49/4 inside the parentheses:
x² + 7x + 49/4 - 49/4 + 12 = 0
(x + 7/2)² = 1/4
Taking the square root of both sides and solving for x, we get:
x + 7/2 = ±1/2
x = -7/2 ± 1/2
Therefore, the solutions to the equation 3x² +12=-21x-24 by completing the square are x = -4 and x = -3.
To solve -x²-3x-13 = -2x² by using the quadratic formula, we first need to move all the terms to one side:
-x² + x - 13 = 0
Next, we identify the coefficients a, b, and c:
a = -1, b = 1, c = -13
Substituting these values into the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
x = (-1 ± sqrt(1² - 4(-1)(-13))) / 2(-1)
x = (-1 ± sqrt(1 + 52)) / (-2)
x = (-1 ± sqrt(53)) / (-2)
Therefore, the solutions to the equation -x²-3x-13 = -2x² by using the quadratic formula are approximately x = -3.25 and x = 4.25.
Explanation: