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When faced with a quadratic equation, one common method to check if a specific number is a solution is to use substitution. Substitution involves replacing the variable, often denoted as \(x\), with the given number. This process helps us verify if the equation holds true for that particular value.

• Start by identifying the variable in the equation. In this case, it is \(x\).
• Substitute the given value, here it's 2, into the equation for \(x\).
• Calculate both sides of the equation separately for this value.

This step is crucial because it simplifies the equation to numerical values, which are easy to compare. By substituting, we directly see if both sides of the equation are equal.

The substitution method is straightforward but powerful. It provides a direct way to determine if a specific value satisfies an equation. Here's how it works:- Begin by replacing the variable with the provided number. This transforms the expression from one that requires algebraic manipulation to one that only needs numerical calculation.- Next, compute both sides of the equation. In this quadratic, \(2(2)^2-1\) and \(4 \times 2 - 1\) are the expressions for each side. - Perform these computations: \(2(2)^2 = 8\) minus 1 equals 7, and \(4 \times 2 = 8\) minus 1 also equals 7.The substitution method is particularly useful not only in checking solutions for equations but in other operations where determining equivalence is necessary. Ensure calculations are accurate to verify the solution correctly.

Once both sides of the equation have been worked out, the next step is verification. Verification involves checking if the results match. If both sides of the equation yield the same result after substitution, then the value is a solution. For our quadratic equation:- Left side after substitution and calculation: 7- Right side after substitution and calculation: 7If these are equal, it means the given number is indeed a solution. In this case, because both sides returned the same value of 7, we conclude that 2 is a valid solution for the equation \(2 x^{2} - 1 = 4 x - 1\). Verification is a key stage, as it confirms the accuracy of both the substitution and subsequent calculations, providing confidence in the solution.