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The solution of the equation is expressed as x = 10 and x = 0.
To solve the equation 0 = x² - 10x + 30, we can complete the square by adding and subtracting the square of half of the coefficient of the x term. In this case, we would add and subtract (1/2 * -10)²= 25 to obtain:
0 = (x - 5)² - 25
This simplifies to x - 5 = +/- √(25), so the solutions to the equation are x = 5 + √(25) and x = 5 - √(25). that is x = 10 and x = 0.
The product (3 + 3i)(3 - 3i) can be calculated by multiplying the terms together, which gives 9 + 9i - 9i - 9i²2. Since i²= -1, this simplifies to 9 - 9i - 9(-1) = 9 + 9i + 9 = 18 + 9i.
To factor the expression 16x² + 25, we can write it as 16x²2 + 4 * 6 + 1 * 25. The expression can then be factored as 16x^2 + 4(6 + 1 * 25), which simplifies to 16x²+ 4(31) = 4(4x² + 31). This shows that the expression 16x² + 25 can be written as the product of 4 and 4x² + 31.
The product (4 + i)(4 - i) can be calculated by multiplying the terms together, which gives 16 - 4i - 4i + i². Since i² = -1, this simplifies to 16 + 4 - 4 - 1 = 11. So the product (4 + i)(4 - i) can be written as 11.
The quotient 101 + 2i can be written in the form a + bi by dividing the numerator by the denominator. In this case, the numerator is 101 + 2i and the denominator is 1, so the quotient is 101 + 2i.
In the complex number system, i is the imaginary unit, which is defined such that i² = -1. Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.
Learn more about Complex number system at:
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