Find the number of real-number solutions of the equation.
2x^2 = 37

Step-by-step explanation:

2x^2 = 37

x^2=37/2

x^2=18.5

=

x=4.301

the answer is d. (1.2, -4.7) on edgn

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4