If the square of a number is added to 8 times the number, the result is 100.

Let's take the number as 'x'.

We are given that, 8x + x² = 100

Now, let's solve for x.

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Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x²+bx=c.

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left-hand side of the equation a perfect square.

Square 4.

Add 100 to 16.

Factor x²+8x+16. In general, when x²+bx+c is a perfect square, it can always be factored as .

Take the square root of both sides of the equation.

Simplify.

Subtract 4 from both sides of the equation.

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step-by-step explanation:

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°