Question

solve the following question in the both the form by completing square .
${x}^{2} + 13x - 30 = 0$
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Answer 1

x² + 13x - 30 = 0

x² + 13x = 30

x² + 13x + 169/4 = 30 + 169/4

(x + 13/2)² = (120 + 169) / 4

(x + 13/2)² = 289/4

x + 13/2 = ±√(289/4)

x + 13/2 = ± 17/2

x = (± 17 - 13) / 2

x = (17 - 13) / 2 OR x = (- 17 - 13) / 2

x = 4/2 OR x = - 30/2

x = 2 OR x = -15

Hence solved!

Explanation of the method:

→ Since the coefficient of x² is 1, we don't need to divide the sides by the coefficients of x², so skip it!

→ Subtract the free term (coefficient of x^0) from both sides. Here the free term is -30, so subtracting -30 means adding 30.

→ Now add the square of half the coefficient of x to both sides, here it's (13/2)² = 169/4.

→ Factorise the LHS and simplify the RHS. We get (x - 13/2)² = 289/4.

→ Take the square root of both sides and subtract 13/2 from both sides.

→ Finally we get the two solutions, 2 and -15.