Final answer:
The constants b and c in the binomial square of the quadratic equation x²+(2.6)x+3.6 are 1.3 and 1.91, respectively. The sum of b and c, which is b+c, is calculated to be 3.21 as a decimal.
Step-by-step explanation:
The question requires rewriting the quadratic equation x²+(2.6)x+3.6 in the form (x+b)²+c, where b and c are constants. To find b, we need to determine the coefficient that will make the x-term in the binomial square equivalent to the x-term in the original equation. The general formula for expanding a binomial is (x+b)² = x² + 2bx + b². We compare this to our original equation to find that 2b must be equal to 2.6, so b = 2.6/2 = 1.3.
Now, we calculate c by determining the constant term in the binomial square. We have b² = 1.3² = 1.69. To get the original constant term of the quadratic, we now subtract b² from the constant term in the quadratic, resulting in 3.6 - 1.69 = 1.91. Therefore, c = 1.91.
Finding the sum b+c, we add 1.3 + 1.91 to get 3.21 as a decimal.