Question

Given the function h(x)=10x2−21x, solve for h(x)=−2.

Give an exact answer; do not round.
(Use a comma to separate multiple solutions.)

x=___

Answer 1

To solve the equation h(x) = -2 for the given function h(x) = 10x^2 - 21x, we need to set the function equal to -2 and solve for x:

10x^2 - 21x = -2

Now, we'll move all terms to one side of the equation to set it to zero:

10x^2 - 21x + 2 = 0

This is a quadratic equation. To solve it exactly, you can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 10, b = -21, and c = 2. Plugging these values into the formula:

x = (-(-21) ± √((-21)² - 4 * 10 * 2)) / (2 * 10)

x = (21 ± √(441 - 80)) / 20

x = (21 ± √361) / 20

x = (21 ± 19) / 20

Now, we have two possible solutions:

1. x = (21 + 19) / 20 = 40 / 20 = 2
2. x = (21 - 19) / 20 = 2 / 20 = 1/10

So, the exact solutions for h(x) = -2 are x = 2 and x = 1/10.

Hope I helped you :)

Answer 2

x = 1/10, 2

Explanation:

You want the solution to h(x) = -2, given h(x) = 10x² -21x.

Zeros

The solution will be found by finding the zeros of ...

10x² -21x = -2

10x² -21x +2 = 0

They can be found by factoring:

(10x -20)(10x -1)/10 = 0

(x -2)(10x -1) = 0

The factors will be zero when ...

x -2 = 0 ⇒ x = 2

10x -1 = 0 ⇒ x = 1/10

The exact solutions to h(x) = -2 are x = 1/10 and x = 2.

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Additional comment

The constants -20 and -1 in the initial factoring are divisors of 10·2 = 20 that have a sum of -21. The product 20 is the product of the leading coefficient and the constant. The sum -21 is the coefficient of the linear term.

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