Here are the essential concepts you must grasp in order to answer the question correctly.
Substitution Method
The substitution method involves replacing a variable or expression with another variable to simplify the equation. In this case, substituting a new variable for √x can transform the equation into a more manageable quadratic form, making it easier to solve.
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Quadratic Equations
A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants. Understanding how to identify and solve quadratic equations is crucial, as they often arise from substitutions in algebraic problems, allowing for the application of factoring, completing the square, or the quadratic formula.
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Factoring
Factoring is the process of breaking down an expression into simpler components, or factors, that can be multiplied together to obtain the original expression. In solving quadratic equations, factoring can provide a quick way to find the roots of the equation, especially when the equation can be expressed as a product of binomials.
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