What are the solutions to the equation completesquare 49x^2-7x-3/4 ?

The solutions to the equation completesquare 49x^2-7x-3/4 are 49(x-1/14)^2-1

Find the zeros of completesquare 49x^2-7x-3/4

The zeros of completesquare 49x^2-7x-3/4 are 49(x-1/14)^2-1

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complete the square

49 x^{2} - 7 x - \frac{3}{4}

49 (x - \frac{1}{14})^{2} - 1

Solution steps

49 x^{2} - 7 x - \frac{3}{4}

Write

49 x^{2} - 7 x - \frac{3}{4}

in the form:

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

Factor out

49

49 (x^{2} - \frac{x}{7} - \frac{3}{196})

2 a = - \frac{1}{7} : a = - \frac{1}{14}

Add and subtract

(- \frac{1}{14})^{2}

49 (x^{2} - \frac{x}{7} - \frac{3}{196} + (- \frac{1}{14})^{2} - (- \frac{1}{14})^{2})

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

x^{2} - \frac{1}{7} x + (- \frac{1}{14})^{2} = (x - \frac{1}{14})^{2}

49 ((x - \frac{1}{14})^{2} - \frac{3}{196} - (- \frac{1}{14})^{2})

Simplify

49 (x - \frac{1}{14})^{2} - 1

5 x^{2} + 3 x + 7 = 0

(m + 4) x^{2} - 2 m x + 2 = 0

- t^{2} + 78 t + 460 = 1581

12 x^{2} + 24 = - 40

5 (x^{2} - 3 x - 4) = (x^{2} - 2 x - 3) \cdot 4

What are the solutions to the equation completesquare 49x^2-7x-3/4 ?
The solutions to the equation completesquare 49x^2-7x-3/4 are 49(x-1/14)^2-1
Find the zeros of completesquare 49x^2-7x-3/4
The zeros of completesquare 49x^2-7x-3/4 are 49(x-1/14)^2-1