What are the solutions to the equation completesquare-4x^2-7x+9 ?

The solutions to the equation completesquare-4x^2-7x+9 are -4(x+7/8)^2+193/16

Find the zeros of completesquare-4x^2-7x+9

The zeros of completesquare-4x^2-7x+9 are -4(x+7/8)^2+193/16

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complete the square

- 4 x^{2} - 7 x + 9

- 4 (x + \frac{7}{8})^{2} + \frac{193}{16}

Solution steps

- 4 x^{2} - 7 x + 9

Write

- 4 x^{2} - 7 x + 9

in the form:

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

Factor out

- 4

- 4 (x^{2} + \frac{7 x}{4} - \frac{9}{4})

2 a = \frac{7}{4} : a = \frac{7}{8}

Add and subtract

(\frac{7}{8})^{2}

- 4 (x^{2} + \frac{7 x}{4} - \frac{9}{4} + (\frac{7}{8})^{2} - (\frac{7}{8})^{2})

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

x^{2} + \frac{7}{4} x + (\frac{7}{8})^{2} = (x + \frac{7}{8})^{2}

- 4 ((x + \frac{7}{8})^{2} - \frac{9}{4} - (\frac{7}{8})^{2})

Simplify

- 4 (x + \frac{7}{8})^{2} + \frac{193}{16}

2 x^{2} + 8 x

x^{2} - x - 1 = 0

y^{2} + 14 y + 48 = 0

(3 x + 1)^{2} + (x + 2)^{2} = 65

2 a^{2} - 5 a + 3 = 0

What are the solutions to the equation completesquare-4x^2-7x+9 ?
The solutions to the equation completesquare-4x^2-7x+9 are -4(x+7/8)^2+193/16
Find the zeros of completesquare-4x^2-7x+9
The zeros of completesquare-4x^2-7x+9 are -4(x+7/8)^2+193/16