Complete the Square x^2+8x-30

Problem

x^2+8*x−30

Solution

1. Identify the coefficient of the linear term x which is 8

2. Calculate the value needed to form a perfect square trinomial by taking half of the linear coefficient and squaring it: (8/2)^2=4^2=16

3. Add and subtract this value within the expression to maintain equality: x^2+8*x+16−16−30

4. Group the first three terms as a perfect square trinomial: (x^2+8*x+16)−16−30

5. Factor the trinomial into its squared binomial form: (x+4)^2−16−30

6. Combine the remaining constant terms: (x+4)^2−46

Final Answer

x^2+8*x−30=(x+4)^2−46

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