1) 2x - 7x^2 + 9 = 0 Rearrange the equation to get: -7x^2 + 2x + 9 = 0 This is a quadratic equation in the form ax^2 + bx + c = 0. Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a We can plug in a = -7, b = 2, c = 9 to get: x = (-(2) ± √((2)^2 - 4(-7)(9))) / 2(-7) x = (-2 ± √(4 + 252)) / -14 x = (-2 ± √256) / -14 x = (-2 ± 16) / -14 x = (-18) / -14 or x = 14/14 x = 9/7 or x = 1
2) 9x^2 - 27 = 0 Add 27 to both sides: 9x^2 = 27 Divide by 9: x^2 = 3 Take the square root of both sides: x = ±√3
3) 8 - 2c^2 = 0 Add 2c^2 to both sides: 2c^2 = 8 Divide by 2: c^2 = 4 Take the square root of both sides: c = ±2
Therefore, the solutions to the equations are: x = 9/7, 1, ±√3 c = ±2
Let's solve the equations step by step.
1) 2x - 7x^2 + 9 = 0
Rearrange the equation to get:
-7x^2 + 2x + 9 = 0
This is a quadratic equation in the form ax^2 + bx + c = 0.
Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
We can plug in a = -7, b = 2, c = 9 to get:
x = (-(2) ± √((2)^2 - 4(-7)(9))) / 2(-7)
x = (-2 ± √(4 + 252)) / -14
x = (-2 ± √256) / -14
x = (-2 ± 16) / -14
x = (-18) / -14 or x = 14/14
x = 9/7 or x = 1
2) 9x^2 - 27 = 0
Add 27 to both sides:
9x^2 = 27
Divide by 9:
x^2 = 3
Take the square root of both sides:
x = ±√3
3) 8 - 2c^2 = 0
Add 2c^2 to both sides:
2c^2 = 8
Divide by 2:
c^2 = 4
Take the square root of both sides:
c = ±2
Therefore, the solutions to the equations are:
x = 9/7, 1, ±√3
c = ±2