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Q: What is finding all solutions of the equation by using mental math or the properties of equality called?

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You are finding the roots or solutions. These are the values of the variable such that the quadratic equation is true. In graphical form, they are the values of the x-coordinates where the graph intersects the x-axis.

When you graph the quadratic equation, you have three possibilities... 1. The graph touches x-axis once. Then that quadratic equation only has one solution and you find it by finding the x-intercept. 2. The graph touches x-axis twice. Then that quadratic equation has two solutions and you also find it by finding the x-intercept 3. The graph doesn't touch the x-axis at all. Then that quadratic equation has no solutions. If you really want to find the solutions, you'll have to go to imaginary solutions, where the solutions include negative square roots.

Yes. Quite often, if you don't, you'll lose solutions. That is, the transformed equation - after taking square roots - will have less solutions than the original equation.

Without an equality sign the given expression can't be classed as an equation and so therefore finding the value of x is not possible.

ambot cniu nmang kot gnie kmu. . . . . . . . .

Depends on degree of highest term. a^3 + bX^2 + cX + d = 0 has three solutions. And so on. Finding them is another matter.

How about finding the solutions of the quadratic equation: x^2-14x+49 = 0

You could try setting the function equal to zero, and finding all the solutions of the equation. Just a suggestion.

the equation for finding pH is pH=log- (negative)

Without an equality sign and not knowing the plus or minus values of y and 7 it can't be considered to be a straight line equation therefore finding its perpendicular equation is impossible.

It very much depends on the equation. The procedure for solving an equation with just one variable is so very different from the procedure for finding solutions to non-linear equations in several variables.

Without an equality sign the given terms can't be classed as an equation and so therefore finding the value of x is not possible.

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