Solve the following problem:
Solve the following problem:
\( (2x+3)(2x-3)=7 \)
Solve for x:
\( (x+1)(2x+1)=2x^2+4 \)
\( (x+1)(x+3)-x=x^2 \)
Solve the following problem:
Solve the following equation. First, we'll simplify the algebraic expressions by using the abbreviated multiplication formula for difference of squares:
We will then apply the mentioned rule and open the parentheses in the expression in the equation:
In the final stage, we distributed the exponent over the parentheses to both multiplication terms inside the parentheses, according to the laws of exponents:
Let's continue and combine like terms, by moving terms:
Next - we can observe that the equation is of the second degree and that the coefficient of the first-degree term is 0. Hence we'll try to solve it using repeated use (in reverse) of the abbreviated multiplication formula for the difference of squares mentioned earlier:
From here remember that the product of expressions will yield 0 only if at least one of the multiplying expressions equals zero,
Therefore we obtain two simple equations and we'll proceed to solve them by isolating the unknown in each:
or:
Let's summarize the solution to the equation:
Therefore the correct answer is answer B.
Solve for x:
Let's solve the equation, first we'll simplify the algebraic expressions using the extended distribution law:
We will therefore apply the mentioned law and open the parentheses in the expression in the equation:
We'll continue and combine like terms, by moving terms, then - we can notice that the term with the squared power cancels out and therefore it's a first-degree equation, which we'll solve by isolating the variable term on one side and dividing both sides of the equation by its coefficient:
Therefore, the correct answer is answer B.
Let's solve the equation, first we'll simplify the algebraic expressions using the extended distribution law:
We will therefore apply the mentioned law and open the parentheses in the expression in the equation:
We'll continue and combine like terms, by moving terms, then - we can notice that the squared term cancels out and therefore it's a first-degree equation, which we'll solve by isolating the variable term on one side and dividing both sides of the equation by its coefficient:
Therefore, the correct answer is answer A.