does anybody know how 1.04(cosA)^2 + 0.2(cosA) -0.75 = 0 become (cosA)^2 + 0.192(cosA) - 0.721 = 0
Are you kidding?
1.04 ( cos A )² + 0.2 ( cos A ) - 0.75 = 0
Divide both sides by 1.04
1.04 ( cos A )² / 1.04 + 0.2 ( cos A ) / 1.04 - 0.75 / 1.04 = 0 / 1.04
( 1.04 / 1.04 ) ∙ ( cos A )² + ( 0.2 / 1.04 ) ∙ ( cos A ) - 0.75 / 1.04 = 0
1 ∙ ( cos A )² + ( 0.2 / 1.04 ) ∙ ( cos A ) - 0.75 / 1.04 = 0
( cos A )² + 0.19231 ( cos A ) - 0.72115 = 0
approx.
( cos A )² + 0.192 ( cos A ) - 0.721 = 0
Magic math.
To understand how the equation 1.04(cosA)^2 + 0.2(cosA) - 0.75 = 0 becomes (cosA)^2 + 0.192(cosA) - 0.721 = 0, let's break it down step by step:
1. Start with the given equation: 1.04(cosA)^2 + 0.2(cosA) - 0.75 = 0
2. Now, let's try to eliminate the decimal point in the coefficient 1.04 by multiplying the entire equation by 100:
100 * [1.04(cosA)^2 + 0.2(cosA) - 0.75] = 100 * 0
Simplifying, we get: 104(cosA)^2 + 20(cosA) - 75 = 0
3. Next, let's deal with the coefficient 104. To simplify the equation, divide the entire equation by 104:
(1/104) * [104(cosA)^2 + 20(cosA) - 75] = (1/104) * 0
Simplifying, we get: (cosA)^2 + (20/104)(cosA) - (75/104) = 0
4. Now, let's simplify the fraction (20/104) by dividing both the numerator and denominator by their greatest common divisor, which is 4:
(cosA)^2 + (5/26)(cosA) - (75/104) = 0
5. Simplifying further, we have:
(cosA)^2 + 0.192(cosA) - 0.721 = 0
Thus, the equation 1.04(cosA)^2 + 0.2(cosA) - 0.75 = 0 becomes (cosA)^2 + 0.192(cosA) - 0.721 = 0 after simplification and elimination of decimals.