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The quadratic x²+(2.6)x+3.6 can be written in the form (x+b)²+c, where b and c are constants. What is b+c (as a decimal)?

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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.

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