Solve Using the Quadratic Formula 4x^2-17x-15=0

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Algebra

$4 x^{2} - 17 x - 15 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 4$ , $b = - 17$ , and $c = - 15$ into the quadratic formula and solve for $x$ .

$\frac{17 \pm \sqrt{{(- 17)}^{2} - 4 \cdot (4 \cdot - 15)}}{2 \cdot 4}$

Simplify.

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Simplify the numerator.

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Raise $- 17$ to the power of $2$ .

$x = \frac{17 \pm \sqrt{289 - 4 \cdot 4 \cdot - 15}}{2 \cdot 4}$

Multiply $- 4$ by $4$ .

$x = \frac{17 \pm \sqrt{289 - 16 \cdot - 15}}{2 \cdot 4}$

Multiply $- 16$ by $- 15$ .

$x = \frac{17 \pm \sqrt{289 + 240}}{2 \cdot 4}$

Add $289$ and $240$ .

$x = \frac{17 \pm \sqrt{529}}{2 \cdot 4}$

Rewrite $529$ as $23^{2}$ .

$x = \frac{17 \pm \sqrt{23^{2}}}{2 \cdot 4}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{17 \pm 23}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{17 \pm 23}{8}$

The final answer is the combination of both solutions.

$x = 5, - \frac{3}{4}$

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Name

Name	one billion sixty-three million one hundred ninety-nine thousand two hundred thirty-five

Interesting facts

1063199235 has 16 divisors, whose sum is 1297102848
The reverse of 1063199235 is 5329913601
Previous prime number is 1607

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 39
Digital Root 3

Name

Name	nine hundred forty-nine million six hundred sixty-seven thousand one hundred eight

Interesting facts

949667108 has 16 divisors, whose sum is 2149396020
The reverse of 949667108 is 801766949
Previous prime number is 169

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 50
Digital Root 5

Name

Name	one billion three hundred twelve million six hundred ninety-nine thousand five hundred fifty-two

Interesting facts

1312699552 has 64 divisors, whose sum is 9968312466
The reverse of 1312699552 is 2559962131
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 43
Digital Root 7

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Evaluate log base 6 of 20