Solve 2x²-12+36=0 by completing the square
2x^2 - 12x + 36 = 0
x^2 - 6x + 18 = 0
x^2 - 6x + 9 = -9
(x-3)^2 = -9
x = 3±3i
To solve the quadratic equation 2x² - 12x + 36 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
2x² - 12x = -36
Step 2: Divide the entire equation by the coefficient of x² (which is 2 in this case):
x² - 6x = -18
Step 3: Take half of the coefficient of x and square it:
Half of -6 is -3, and (-3)² is 9.
Step 4: Add the square from Step 3 to both sides of the equation:
x² - 6x + 9 = -18 + 9
x² - 6x + 9 = -9
Step 5: Rewrite the left side of the equation as a perfect square trinomial:
(x - 3)² = -9
Step 6: Take the square root of both sides of the equation:
√((x - 3)²) = ±√(-9)
Step 7: Simplify the square root of -9:
√(-9) = ±3i√1
Step 8: Solve for x:
(x - 3) = ±3i
x = 3 ± 3i
Therefore, the solutions to the equation 2x² - 12x + 36 = 0 by completing the square are x = 3 + 3i and x = 3 - 3i.