solve by completing the square; round to the nearest hundreth, if necessary.x^2-3x=4

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should notice that it misses one squared term to the left side, for the square to be completed, hence, you need to use the following formula to identify the missing term, such that:

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

Identifying `a^2 = x^2` and `3x = 2ab` , you may find `b^2` such that:

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

Substituting x for a in `2ab = 3x` yields:

`2xb = 3x`

Reducing duplicate terms yields:

`2b = 3 => b = 3/2 => b^2 = 9/4`

Hence, you need to add `9/4` to the left side, to complete the square and you also need to add `9/4` to the right side, to preserve the equality, such that:

`x^2 - 3x + 9/4 = 4 + 9/4`

`(x - 3/2)^2 = 25/4 => x - 3/2 = +-(5/2)`

`x_1 = 3/2 + 5/2 => x_1 = 8/2 => x_1 = 4`

`x_2 = 3/2 - 5/2 => x_2 = -2/2 => x_2 = -1`

Hence, evaluating the solutions to the given quadratic equation, completing the square, yields `x_1 = 4` and `x_2 = -1` .

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