A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: $(a-b)^2=a^2-2ab+b^2$
$x^2+x^2-2x+1=3$
2
Combining like terms $x^2$ and $x^2$
$2x^2-2x+1=3$
3
Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side
$2x^2-2x=3-1$
4
Subtract the values $3$ and $-1$
$2x^2-2x=2$
5
Rewrite the equation
$2x^2-2x-2=0$
6
Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($2$) to all terms
$2\left(x^2-x-1\right)=0$
7
Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$
$2\left(x^2-x-1+\frac{1}{4}-\frac{1}{4}\right)=0$
8
Factor the perfect square trinomial $x^2+-xx+\frac{1}{4}$
As in the equation we have the sign $\pm$, this produces two identical equations that differ in the sign of the term $\sqrt{\left(\frac{5}{4}\right)}$. We write and solve both equations, one taking the positive sign, and the other taking the negative sign
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more
Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.