To solve each equation, we can use the quadratic formula:
For the equation x^2 - 4x - 96 = 0, a = 1, b = -4, c = -96 x = (-b ± √(b^2 - 4ac)) / 2a x = (4 ± √((-4)^2 - 41(-96))) / 2*1 x = (4 ± √(16 + 384)) / 2 x = (4 ± √400) / 2 x = (4 ± 20) / 2 x = (4 + 20) / 2 or x = (4 - 20) / 2 x = 24 / 2 or x = -16 / 2 x = 12 or x = -8
Therefore, the solutions to x^2 - 4x - 96 = 0 are x = 12 and x = -8.
For the equation 2x^2 + 8x - 24 = 0, a = 2, b = 8, c = -24 x = (-8 ± √(8^2 - 42(-24))) / 2*2 x = (-8 ± √(64 + 192)) / 4 x = (-8 ± √256) / 4 x = (-8 ± 16) / 4 x = (8 + 16) / 4 or x = (8 - 16) / 4 x = 24 / 4 or x = -8 / 4 x = 6 or x = -2
Therefore, the solutions to 2x^2 + 8x - 24 = 0 are x = 6 and x = -2.
For the equation -x^2 + 3x + 18 = 0, a = -1, b = 3, c = 18 x = (-3 ± √(3^2 - 4(-1)18)) / 2*(-1) x = (-3 ± √(9 + 72)) / -2 x = (-3 ± √81) / -2 x = (-3 ± 9) / -2 x = (6) / -2 or x = (-12) / -2 x = -3 or x = 6
Therefore, the solutions to -x^2 + 3x + 18 = 0 are x = -3 and x = 6.
To solve each equation, we can use the quadratic formula:
For the equation x^2 - 4x - 96 = 0,
a = 1, b = -4, c = -96
x = (-b ± √(b^2 - 4ac)) / 2a
x = (4 ± √((-4)^2 - 41(-96))) / 2*1
x = (4 ± √(16 + 384)) / 2
x = (4 ± √400) / 2
x = (4 ± 20) / 2
x = (4 + 20) / 2 or x = (4 - 20) / 2
x = 24 / 2 or x = -16 / 2
x = 12 or x = -8
Therefore, the solutions to x^2 - 4x - 96 = 0 are x = 12 and x = -8.
For the equation 2x^2 + 8x - 24 = 0,
a = 2, b = 8, c = -24
x = (-8 ± √(8^2 - 42(-24))) / 2*2
x = (-8 ± √(64 + 192)) / 4
x = (-8 ± √256) / 4
x = (-8 ± 16) / 4
x = (8 + 16) / 4 or x = (8 - 16) / 4
x = 24 / 4 or x = -8 / 4
x = 6 or x = -2
Therefore, the solutions to 2x^2 + 8x - 24 = 0 are x = 6 and x = -2.
For the equation -x^2 + 3x + 18 = 0,
a = -1, b = 3, c = 18
x = (-3 ± √(3^2 - 4(-1)18)) / 2*(-1)
x = (-3 ± √(9 + 72)) / -2
x = (-3 ± √81) / -2
x = (-3 ± 9) / -2
x = (6) / -2 or x = (-12) / -2
x = -3 or x = 6
Therefore, the solutions to -x^2 + 3x + 18 = 0 are x = -3 and x = 6.