To solve the equation \(-x^2 + 5x = -x + 5\), we can first simplify and rearrange it.
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Start by bringing all terms to one side of the equation: \[ -x^2 + 5x + x - 5 = 0 \] This simplifies to: \[ -x^2 + 6x - 5 = 0 \]
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Multiply the entire equation by -1 to make the leading coefficient positive: \[ x^2 - 6x + 5 = 0 \]
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Now, we factor the quadratic equation: \[ (x - 1)(x - 5) = 0 \] This gives us two solutions: \[ x - 1 = 0 \implies x = 1 \] \[ x - 5 = 0 \implies x = 5 \]
So the solutions to the equation are \(x = 1\) and \(x = 5\).
From the responses provided (0, -6, 1, 4), the correct value of \(k\) that is a solution to the equation is \(1\).
1 answer