Question

Write 2x² +16x+85 in the form a(x + b)²+c, where a, b and c are integers (whole numbers) to be found.

Answer 1

Ответ:

2(x+4)²+53

a=2, b=4, c=53

Пошаговое объяснение:

a(x + b)²+c, a=?  b=?  c=?

2x²+16x+85=(2x²+16x)+85= 2(x²+8x)+85=2(x²+2*4x+4²)-2*4²+85=

=2(x+4)²-32+85=2(x+4)²+53

a=2, b=4, c=53

Answer 2

To write the quadratic expression 2x² + 16x + 85 in the form a(x + b)² + c, we'll complete the square. Here's the process step by step:

1. Start with the given quadratic expression: 2x² + 16x + 85.

2. First, factor out the coefficient of the x² term (which is 2) from the x² and x terms: 2(x² + 8x) + 85

3. Now, focus on the expression inside the parentheses, x² + 8x. To complete the square, we need to add and subtract a value that will make it a perfect square trinomial. To do this, take half of the coefficient of the x term (8/2 = 4) and square it (4² = 16). Add and subtract 16 inside the parentheses:

   2(x² + 8x + 16 - 16) + 85

4. Now, rewrite the expression, factoring the perfect square trinomial:

   2((x + 4)² - 16) + 85

5. Distribute the 2 into the parentheses:

   2(x + 4)² - 2(16) + 85

6. Simplify the expression further:

   2(x + 4)² - 32 + 85

7. Combine the constants:

   2(x + 4)² + 53

So, the expression 2x² + 16x + 85 can be written in the form a(x + b)² + c as 2(x + 4)² + 53, where a = 2, b = 4, and c = 53.