Question

If $x^2+3x=10$, which of the following is a possible value of $x$ ? (A) $-2$ (B) 5 (C) 7 (D) $-5$

Short answer

The correct answer is (D) $x=-5$.

Step-by-step solution

Rewrite the Equation

Rewrite the given equation as $x^2+3x-10=0$.

Evaluate Each Option

Now we will check each answer choice and see if they satisfy the equation: (A) $x=-2$ $(-2{)}^2+3(-2)-10=4-6-10=-12$, so this is not a solution. (B) $x=5$ $(5{)}^2+3(5)-10=25+15-10=30$, so this is not a solution. (C) $x=7$ $(7{)}^2+3(7)-10=49+21-10=60$, so this is not a solution. (D) $x=-5$ $(-5{)}^2+3(-5)-10=25-15-10=0$, so this is a solution. Thus, the correct answer is (D) $x=-5$.

Key concepts

Solving Equations

To solve an equation, especially a quadratic one like the given example, we need to rearrange terms and find the values of variables that satisfy the equation. Quadratic equations are typically in the form of $a{x}^2+bx+c=0$. Your goal is to find the value of $x$ that makes this equation true. In the given exercise:
$x^2+3x=10$, this can be rewritten as $x^2+3x-10=0$ by moving the term 10 to the left side.

• The solutions or roots of the quadratic equations are the values of $x$ that satisfy this equation.
• Sometimes, these solutions can be found by factorization or by using a quadratic formula.

However, in our problem, we try each solution option to see which value, when plugged into the equation, results in the equation balancing to zero.
This process may involve testing different numbers or utilizing algebraic techniques like factoring.

Algebra

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In quadratic equations, algebra helps in organizing and simplifying expressions. The given equation involves algebraic steps. By rewriting $x^2+3x=10$ as $x^2+3x-10=0$, we transform the expression into a standard quadratic form. This allows us to use algebraic methods to solve it.

Basic algebraic principles help us to:

• Combine like terms and move terms across an equation.
• Understand variable behavior and find their numerical equivalents.
• Simplify expressions to determine solutions efficiently.

Algebra provides the toolkit to both construct equations and solve them, a critical skill for all math-enthusiasts.

GED Math Practice

GED math practice involves multiple math skills including understanding and solving quadratic equations as well as other algebraic formulas. Practical problem-solving is crucial in preparing for the GED exams. Quadratic equations, being a significant part, are almost always featured in practice tests. Here's how practicing problems like this helps:

• Improves your ability to identify different types of equations.
• Develops your understanding of important mathematical operations.
• Equips you with strategies to tackle a diverse range of math questions.

As you prepare for the GED test, tackling a range of problems, including those involving quadratic equations, will build your confidence. It ensures you develop a deeper understanding and can skillfully solve problems under test conditions. This exercise exemplifies the typical complexity level of actual GED questions you might encounter.