b = 20 and b = -20
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In order for the quadratic equation to have one real solution, the discriminant (b² - 4ac) must equal zero.
Using the values a = 4, b = b, and c = 25, we substitute them into the discriminant formula and set it equal to zero:
- (b² - 4ac) = 0
- b² - 4(4)(25) = 0
- b² - 400 = 0
- b² = 400
- b = ± √400
- b = ± 20
Therefore, the values of b that will cause the equation to have one real solution are b = 20 and b = -20.