2*cosx*(2x+30°) + √3=0
2 answers:
Answer: x ≈ 1.59688927, −1.60312387, −4.67045686, 4.69039614, 7.872914, −7.91513776, −10.89002194
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Simplify 2*cosx*(2x+30°) + √3=0
Simplify each term.
Apply the distributive property.
- 2 cos ( x ) ( 2 x ) + 2 cos ( x ) * 30 ° + √ 3 = 0
- Multiply 2 by 2
- 4 cos ( x ) x + 2 cos ( x ) *30 ° + √ 3 = 0
- Multiply 30 °by 2
- 4 cos ( x ) x + 60 cos ( x ) + √ 3 = 0
- Reorder factors in 4 cos ( x ) x + 60 cos ( x ) + √3
- 4xcos(x)+60cos(x)+√3=0
- Graph each side of the equation. The solution is the x-value of the point of intersection. x ≈ 1.59688927 , − 1.60312387 , − 4.67045686 , 4.69039614 , 7.872914 , − 7.91513776 , − 10.89002194
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Answer:
2 real solutions
Step-by-step explanation:
Remember this messy thing?
The <em>quadratic formula</em>, as it's called, gives us the roots to any quadratic equation in standard form (ax² + bx + c = 0). The information on the <em>type</em> of roots is contained entirely in that bit under the square root symbol (b² - 4ac), called the <em>discriminant</em>. If it's non-negative, we'll have <em>real</em> roots, if it's negative, we'll have <em>complex roots</em>.
For our equation, we have a discrimant of (-3)² - 4(6)(-4) = 9 + 96 = 105, which is non-negative, so we'll have real solutions, and since quadratics are degree 2, we'll have exactly 2 real solutions.