🧮 algebra

1. Bài toán: Giải phương trình bậc hai dạng tổng quát $$ax^2 + bx + c = 0$$ với $$a \neq 0$$. 2. Công thức nghiệm: Sử dụng công thức nghiệm của phương trình bậc hai:

1. **State the problem:** Solve the quadratic equation $$2x^2 - 3 = 5x$$ for $$x$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. El problema consiste en desarrollar cada binomio al cuadrado usando la fórmula del cuadrado de una diferencia o suma: $$ (A \pm B)^2 = A^2 \pm 2AB + B^2 $$ 2. Aplicamos la fórmu

1. **Problem statement:** Decompose each expression as a perfect square trinomial. 2. **Formula used:** For any binomial $(A \pm B)^2 = A^2 \pm 2AB + B^2$.

1. **State the problem:** We have a sequence starting at $10$. The rule to get from one term to the next is: subtract $3$ then multiply by $2$.

1. **State the problem:** We have a sequence where each term is the sum of the previous two terms. The sequence starts as $3, \_, 7, \_, \_, 29, ...$ and we need to find the three

1. **Simplify** $7\sqrt{11} \times 3\sqrt{11}$. The problem asks us to multiply two terms involving square roots.

1. **State the problem:** Lia wants to buy shoes priced at $35 from three stores offering different discounts. We need to find the sale price at each store and verify the truth of

1. **State the problem:** We need to determine the final price a customer pays after applying two different discount options to a car originally priced at $22,860. 2. **Formulas an

1. Simplify the expression $$\sqrt{50}$$. 2. Solve for $x$: $$\sqrt{x+5} = 7$$.

1. **State the problem:** Solve the equation $$4^{2x-1} = 64$$ for $$x$$. 2. **Recall the formula and rules:** We know that $$a^{m} = a^{n}$$ implies $$m = n$$ if $$a > 0$$ and $$a

1. **Stating the problem:** Solve for $x$ in the equation $5^x = 625$. 2. **Recall the formula:** When you have an equation of the form $a^x = b$, you can solve for $x$ by expressi

1. **State the problem:** Simplify or factor the quadratic expression $$X^2 + 9x - 400$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look

1. Let's clarify what an intercept means in algebra. 2. The intercept usually refers to the point where a graph crosses the axes. The y-intercept is where the graph crosses the y-a

1. **State the problem:** Find the intercepts of the graph of the linear equation $$y=3x+2$$. 2. **Recall the intercepts:**

1. **State the problem:** Factor the expression $$49x^2 - 64y^2$$. 2. **Recognize the formula:** This is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b)(a

1. **State the problem:** We need to evaluate the expression $$(-4)^{-2} \times 2^{5}$$ without using a calculator. 2. **Recall the rules:**

1. **State the problem:** Find the zeros of the cubic polynomial $$8x^3 - 42x^2 + 9x + 5$$ and determine their multiplicities. 2. **Recall the formula and rules:** To find zeros of

1. **State the problem:** Find the zeros of the cubic polynomial $$x^3 - 4x^2 + 9x + 5$$ and determine their multiplicities. 2. **Recall the formula and rules:** To find zeros of a

1. **State the problem:** Solve the equation $$3+0.5(4a+8)=9-2a$$ for the variable $a$. 2. **Write down the equation:** $$3 + 0.5(4a + 8) = 9 - 2a$$

1. **State the problem:** Solve the equation $$-t = 9(t-10)$$ for $t$. 2. **Distribute the 9 on the right side:**