Answer:
x = 0
x = -3
Explanation:
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Thereforeo solve the quadratic equation 8x² + 18x + 0 = 0 using the completing the square method, follow these steps:
Step 1: Divide the entire equation by the coefficient of x² to make the leading coefficient 1:
x² + (18/8)x + 0 = 0
x² + (9/4)x + 0 = 0
Step 2: Take half of the coefficient of x (which is 9/4) and square it:
(9/4) / 2 = 9/8
(9/8)² = 81/64
Step 3: Add and subtract the value from step 2 inside the parentheses:
x² + (9/4)x + 81/64 - 81/64 + 0 = 0
x² + (9/4)x + 81/64 - 81/64 = 0
Step 4: Factor the perfect square trinomial and simplify:
(x + 9/8)² - 81/64 = 0
Step 5: Solve for x by taking the square root of both sides:
(x + 9/8)² = 81/64
x + 9/8 = ±√(81/64)
Step 6: Solve for x:
x = -9/8 ± √(81/64)
x = -9/8 ± 9/8
This gives you two solutions:
x = 0
x = -3
Therefore, the solutions to the quadratic equation 8x² + 18x + 0 = 0 are x = 0 and x = -3.