SOLUTION: Fill in the blanks with numbers to make a true equation.
3x^2 + 12x + 4 - 17x^2 - 18x + 22 = ___ (x + ___)^2 + ___
Algebra.Com
Question 1209268: Fill in the blanks with numbers to make a true equation.
3x^2 + 12x + 4 - 17x^2 - 18x + 22 = ___ (x + ___)^2 + ___
Answer by asinus(45) (Show Source): You can put this solution on YOUR website!
**1. Combine Like Terms**
* 3x² + 12x + 4 - 17x² - 18x + 22
* = (3x² - 17x²) + (12x - 18x) + (4 + 22)
* = -14x² - 6x + 26
**2. Complete the Square**
* **Factor out the coefficient of x²:**
-14(x² + (6/14)x) + 26
-14(x² + (3/7)x) + 26
* **Inside the parentheses, add and subtract the square of half the coefficient of x:**
-14(x² + (3/7)x + (3/14)² - (3/14)²) + 26
* **Rewrite as a perfect square trinomial:**
-14[(x + 3/14)² - 9/196] + 26
* **Distribute -14:**
-14(x + 3/14)² + 126/196 + 26
* **Simplify:**
-14(x + 3/14)² + 30.2857
**Therefore, the equation can be filled in as follows:**
3x² + 12x + 4 - 17x² - 18x + 22 = **-14** (x + **-0.2857**)² + **30.2857**
RELATED QUESTIONS
Fill in the blanks, to make a true equation:
\frac{2x^4 - 3x^3 - x^2 + 4x - 4}{x^2 +... (answered by CPhill)
Fill in the blanks, to make a true equation:
(8x^3 + 24x^2 + 15x + 1)/((x^2 - 1)(x^2 + (answered by Edwin McCravy)
Fill in the blanks with constants, to make a true equation:
\frac{x^2 - 6x - 3}{x^3 -... (answered by CPhill,MathTherapy)
Fill in the blanks with > or < to make the resulting statement true: 2__-9 and
-2(2)__... (answered by waynest)
Fill in the blanks, to make a true equation.
3/(3^2 - 1) + 3^2/(3^4 - 1) +... (answered by ikleyn)
Fill in the blanks with unlike fractions so as to make the equation true... (answered by ankor@dixie-net.com)
Factor by grouping (sometimes called the ac-method).
First, choose a form with... (answered by solver91311)
Can you help me with this?
Fill in the blanks.
a) {{{14x^2-21=(______)(2x^2-3)}}}
b) (answered by checkley77)
Fill in the blanks to make a quadratic whose roots are -5 and 5.
x^2 + ___ x +... (answered by ikleyn,math_tutor2020)