Solve each equation. See Examples 4–6. √2x-x+4=0

Key Concepts

Square Roots

Square roots are the values that, when multiplied by themselves, yield the original number. In the equation √2x - x + 4 = 0, understanding how to manipulate square roots is essential for isolating the variable. This involves recognizing that squaring both sides of an equation can eliminate the square root, but it must be done carefully to avoid extraneous solutions.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax² + bx + c = 0, where a, b, and c are constants. The equation in the question can be rearranged into a quadratic form, allowing the use of methods such as factoring, completing the square, or the quadratic formula to find solutions. Recognizing the structure of a quadratic equation is crucial for solving it effectively.

Isolating Variables

Isolating variables involves rearranging an equation to solve for a specific variable. In the context of the given equation, this means manipulating the terms to get x by itself on one side of the equation. Mastery of this concept is vital for solving equations, as it allows students to systematically approach and simplify complex expressions.