Fact Check: Does x^2 + 1/2x - 7.5 Have Roots 2.5 and -3?

There are no extraneous solutions.

So, x = 0 is not a solution. ... When we substitute x = 3 into the original equation, we get the statement 3 = 3. This is true, so x = 3 is a solution. Solution: x = 3. Note: The solution is the x-coordinate of the intersection point of the graphs of y = x and y = sqrt(x+1)+1.

Solution. The quadratic equation is written in the standard form ... Answer. x = 1 or x = −3 . ... Example 2. Solve the equation 2x2 −3x −1 = 0 .

Beginners often make mistakes when they use "working backward," because they don't notice that some step is irreversible. For instance, the statement · x > is not true for all real numbers x. But if we didn't know that, we might come up with this proof: ... Squaring both sides of an inequality is a reversible step if both sides are nonnegative. Thus we obtain ... x." But that conclusion is wrong. The right side of the inequality is undefined when x = 0.5.

In the first case I put parenthesis around then \(4x - 5\) and in the second I didn’t. Since we are subtracting a polynomial we need to make sure we subtract the WHOLE polynomial! The only way to make sure we do that correctly is to put parenthesis around it. Again, this is one of those errors that people do know that technically the parenthesis should be there, but they don’t put them in and promptly forget that they were there and do the subtraction incorrectly. Example 4 Convert \(\sqrt {7x} \) to fractional exponents.

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Topic TextTopic TermsGlossary

... The computation from Step 6 to Step 7 is not evaluated correctly, because the square root of the discriminant is incorrectly simplified. ... The quadratic formula has many parts in it.

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