Solve the quadratic equation 3x²=27
Solve the quadratic equation 2x² - 4x + 1 = 0
3x²=27
can't get any easier ...
3x^2 = 27
divide both sides by 3
x^2 = 9
x = ± 3
try the second one using either the formula or completing the square.
Let me know your steps
To solve a quadratic equation, we can follow these steps:
Step 1: Set the equation equal to zero.
For the equation 3x² = 27, we already have it set to zero.
For the equation 2x² - 4x + 1 = 0, we need to subtract 1 from both sides to set it equal to zero:
2x² - 4x + 1 - 1 = 0 - 1
2x² - 4x = -1
Step 2: Identify the coefficients a, b, and c.
For 3x² = 27, the coefficient a is 3, b is 0, and c is -27.
For 2x² - 4x = -1, the coefficient a is 2, b is -4, and c is -1.
Step 3: Use the quadratic formula to find the solutions.
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a)
For 3x² = 27, substituting the values into the formula we get:
x = (0 ± √(0 - 4 * 3 * -27)) / (2 * 3)
Simplifying:
x = ±√(0 + 324) / 6
x = ±√324 / 6
x = ±18 / 6
Therefore, the solutions are x = -3 and x = 3.
For 2x² - 4x = -1:
x = (-(-4) ± √((-4)² - 4 * 2 * (-1))) / (2 * 2)
Simplifying:
x = (4 ± √(16 + 8)) / 4
x = (4 ± √24) / 4
x = (4 ± √(4 * 6)) / 4
x = (4 ± 2√6) / 4
Simplifying further, we can divide both the numerator and denominator by their greatest common divisor, which is 2. This gives us:
x = (2 ± √6) / 2
Therefore, the solutions are x = 1 + √6/2 and x = 1 - √6/2.