Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( c=6 \)
Solution
Solve the equation \( 2x^{2}-7x+c=(2x-3)(x-2) \).
Solve the equation by following steps:
- step0: Solve for \(c\):
\(2x^{2}-7x+c=\left(2x-3\right)\left(x-2\right)\)
- step1: Rewrite the expression:
\(2x^{2}-7x+c=2x^{2}-7x+6\)
- step2: Move the expression to the right side:
\(c=2x^{2}-7x+6-\left(2x^{2}-7x\right)\)
- step3: Subtract the terms:
\(c=6\)
The value of \( c \) is 6.
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Simplify this solution Mind Expander
To find \( c \), let's start by expanding the right side of the equation: \[ (2x-3)(x-2) = 2x \cdot x + 2x \cdot (-2) - 3 \cdot x - 3 \cdot (-2) \] \[ = 2x^2 - 4x - 3x + 6 = 2x^2 - 7x + 6 \] Now, we compare this with the left side of the equation: \[ 2x^2 - 7x + c \] From both expressions, we can see that the coefficients of \( x^2 \) and \( x \) match, thus: \[ c = 6 \] Therefore, the value of \( c \) is \( 6 \).
