What are the solutions to the equation completesquare 4x^2-10x-3 ?

The solutions to the equation completesquare 4x^2-10x-3 are 4(x-5/4)^2-37/4

Find the zeros of completesquare 4x^2-10x-3

The zeros of completesquare 4x^2-10x-3 are 4(x-5/4)^2-37/4

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complete the square

4 x^{2} - 10 x - 3

4 (x - \frac{5}{4})^{2} - \frac{37}{4}

Solution steps

4 x^{2} - 10 x - 3

Write

4 x^{2} - 10 x - 3

in the form:

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

Factor out

4

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

2 a = - \frac{5}{2} : a = - \frac{5}{4}

Add and subtract

(- \frac{5}{4})^{2}

4 (x^{2} - \frac{5 x}{2} - \frac{3}{4} + (- \frac{5}{4})^{2} - (- \frac{5}{4})^{2})

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

x^{2} - \frac{5}{2} x + (- \frac{5}{4})^{2} = (x - \frac{5}{4})^{2}

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

Simplify

4 (x - \frac{5}{4})^{2} - \frac{37}{4}

3 (x - 2)^{2} = 7

y^{2} - 9 y + 8 = 0

x, x^{2} + y^{2} - 6 x + 2 y + 12 = 0

(x + 1) (x - 1) = 3

6 x^{2} - 5 x = 6

What are the solutions to the equation completesquare 4x^2-10x-3 ?
The solutions to the equation completesquare 4x^2-10x-3 are 4(x-5/4)^2-37/4
Find the zeros of completesquare 4x^2-10x-3
The zeros of completesquare 4x^2-10x-3 are 4(x-5/4)^2-37/4