Question

question 5 of 10
what two steps are necessary to put this equation into standard form?
$x^2 - 3x + 27 = 8x - 3$

a. the equation is already in standard form.

b. subtract 3 to both sides and subtract 8x from both sides.

c. add 3 to both sides and subtract 8x from both sides.

d. add 3 to both sides and add 8x from both sides.

Explanation:

The standard form of a quadratic equation is \(ax^{2}+bx + c = 0\). For the equation \(x^{2}-3x + 27=8x - 3\), we need to get all terms on one side. First, add 3 to both sides to eliminate the - 3 on the right: \(x^{2}-3x + 27+3=8x - 3 + 3\) which simplifies to \(x^{2}-3x+30 = 8x\). Then, subtract \(8x\) from both sides: \(x^{2}-3x - 8x+30=8x - 8x\), resulting in \(x^{2}-11x + 30 = 0\). So the steps are add 3 to both sides and subtract \(8x\) from both sides.

Answer:

C. Add 3 to both sides and subtract 8x from both sides.