Question

Solve: 25x2 − 30 = 0 round the answer to the nearest hundredth. x = −1.10 and x = 1.10 x = −26.15 and x = 1.15 x = 0 x = −0.83 and x = 0.83

Answer 1

(a) x = -1.10 and x = 1.10

Explanation:

A straightforward square root will give the value of x.

Solution

Divide by the coefficient of x^2:

x^2 -30/25 = 0

x^2 -1.20 = 0

Add 1.20, and take the square root.

x^2 = 1.20

x = ±√1.20 ≈ ±1.0954

x ≈ -1.10 and 1.10 . . . . . round to hundredths

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Additional comment

For small values of x, the root of (1+x) is approximately 1+x/2. For a root accuracy to the nearest hundredth, x < 0.21 (as here). For accuracy to the nearest thousandth, x < 0.064.