Solve for x:x2 = 3x + 10.

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To solve the equationx2=3.v + 10, turn it into an equation equal to 0, find the two factors of the new equation, and then set each factor equal to 0, to solve for x. Step I: Move all expressions to one side of the equal sign. Change the signs of terms that are moved. x2-3x-10 = 0 Step 2: Find the two factors that you would multiply to produce this polynomial. Do this one expression at a time. What gives youx2'?The answer isxtimesx.Therefore place anxat the beginning of each factor. (x )(x ) Next find the two numbers you would multiply to get 10. The)' could be 10 and I, or 5 and 2, but remember that the two numbers also have to produce 3, the middle term in the polynomial. The difference between 5 and 2 is 3. Therefore 5 and 2 are the numbers that complete the factors (x -5)(x + 2) Now decide the signs that belong in each factor. The appearance of -10 in the polynomial means that 5 and 2 have different signs. The -3.v in the polynomial indicates that 5 (the larger number) has the minus sign, and that 2 has a plus sign. Thus (x-5)(x + 2) Step 3: Set each factor equal to zero and solve the equations. x-5=0 x+2=0 x = 5 x = -2

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