<span>x^2 + 15x + 56.25 = 105.25
"Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
So we have
x^2 + 15x + 56.25 = 49 + 56.25
Which is
x^2 + 15x + 56.25 = 105.25
Which is the answer desired.
Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?"
Well, we know that the left hand side of the equation can now be written as
(x+7.5)^2 = 105.25
Now take the square root of each side
(x+7.5) = sqrt(105.25)
And let's use both the positive and negative square roots.
So
x+7.5 = 10.25914226
and
x+7.5 = -10.25914226
And let's find X.
x+7.5 = 10.25914226
x = 2.759142264
x+7.5 = -10.25914226
x = -17.75914226
So the roots for x^2 + 15x - 49 is 2.759142264, and -17.75914226</span>
5 x 6 = 30
9 x 6 = 54
54 + 30 = 84
you would be intaking 84 grams of fat
15
Explanation: Plug in 9 into d which gives you 24-9. Making it 15.
9514 1404 393
Explanation:
When something is subtracted from both sides of the equation, the justification is the <em>subtraction property of equality</em>. When something multiplies both sides of the equation, the justification is the <em>multiplication property of equality</em>. (This should not be a mystery.)
Here, the equation is solved by subtracting 17/3, then subtracting 1/2x, then multiplying by the inverse of the coefficient of x. After each of these steps is a simplification.
26 and 27.
Consecutive numbers are pairs of numbers like 1 and 2 or 5 and 6. One number right after the other to equal the whole number. Subtract 1 from 53 to get 52 then divide 52 by 2 to get 26. Then just add the 1 back on to get 26 and 27 to equal 53.
Hope this helped! :)
