What are the solutions to the equation completesquare 4x^2-28x+49 ?

The solutions to the equation completesquare 4x^2-28x+49 are 4(x-7/2)^2

Find the zeros of completesquare 4x^2-28x+49

The zeros of completesquare 4x^2-28x+49 are 4(x-7/2)^2

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complete the square

4 x^{2} - 28 x + 49

4 (x - \frac{7}{2})^{2}

Solution steps

4 x^{2} - 28 x + 49

Write

4 x^{2} - 28 x + 49

in the form:

x^{2} + 2 a x + a^{2}

Factor out

4

4 (x^{2} - 7 x + \frac{49}{4})

2 a = - 7 : a = - \frac{7}{2}

Add and subtract

(- \frac{7}{2})^{2}

4 (x^{2} - 7 x + \frac{49}{4} + (- \frac{7}{2})^{2} - (- \frac{7}{2})^{2})

x^{2} + 2 a x + a^{2} = (x + a)^{2}

x^{2} - 7 x + (- \frac{7}{2})^{2} = (x - \frac{7}{2})^{2}

4 ((x - \frac{7}{2})^{2} + \frac{49}{4} - (- \frac{7}{2})^{2})

Simplify

4 (x - \frac{7}{2})^{2}

m^{2} - 5 m - 14 = 0

5 n^{2} - 14 = - 6

2 x^{2} + 6 x = 3 + x

x^{2} - x = 6

7 x^{2} + 5 x = - 2

What are the solutions to the equation completesquare 4x^2-28x+49 ?
The solutions to the equation completesquare 4x^2-28x+49 are 4(x-7/2)^2
Find the zeros of completesquare 4x^2-28x+49
The zeros of completesquare 4x^2-28x+49 are 4(x-7/2)^2