x^2-16x=-64

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You may solve the quadratic equation by completing th square to the left side, hence, you need to use the following formula that helps you to decide what is the missing term that completes the square, such that:

`a^2 - 2ab + b^2 = (a - b)^2`

Identifying `a^2 = x^2` and `2ab = 16x` yields:

`a^2 = x^2 => a = x`

`2ab = 16x`

Replacing x for a yields:

`2xb = 16x => 2b = 16 => b = 16/2 => b = 8 => b^2 = 64`

Hence, the missing term that completes the square is 64, thus, you need to add both sides the constant `64` , such that:

`x^2 - 16x + 64 = -64 + 64`

`(x - 8)^2 = 0`

Taking the square root both sides yields:

`x - 8 = 0 => x_1 = x_2 = 8`

Hence, evaluating the solutions to the given quadratic equation, yields `x_1 = x_2 = 8` .

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The equation x^2-16x=-64 has to be solved for x.

x^2-16x=-64

x^2 - 16x + 64 = 0

The solution of a quadratic equation ax^2 + bx + c = 0 is `(-b+-sqrt(b^2 - 4ac))/(2a)` .

Here, a = 1, b = -16 and c = 64

The solution of the equation is `(16+sqrt(256 - 4*1*64))/2 = 8`

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