To solve for x, we can first isolate the variable by solving the equation step by step:
−2(x − 2)² + 5 = 0
Simplify:
−2(x² - 4x + 4) + 5 = 0
Distribute:
−2x² + 8x - 8 + 5 = 0
Combine like terms:
−2x² + 8x - 3 = 0
Rearrange the equation to make it easier to solve:
2x² - 8x + 3 = 0
Now we can solve for x by using the quadratic formula:
x = [-(-8) ± √((-8)² - 4(2)(3))] / 2(2)
x = [8 ± √(64 - 24)] / 4
x = [8 ± √40] / 4
x = (8 ± 6.32) / 4
Therefore, x ≈ 3.58 or x ≈ 0.42. So, the correct answer is:
x = 3.58, 0.42
Solve for x: −2(x − 2)2 + 5 = 0
Round your answer to the nearest hundredth.
x = 3.58, 0.42
x = 4.52, −0.52
x = −3.58, −0.42
x = −4.52, 0.52
1 answer