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# Algebra

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Find all solutions to the equation x^2 - 7x = 38. If you find more than one, then list the values separated by commas.

Jan 18, 2022

#1
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You can rewrite the equation as x^2-7x-38=0, then use the quadratic formula, which leads to the answers x=[7-sqrt(201)]/2 and x=[7+sqrt(201)]/2.

I am pretty sure this is how you do it.

Jan 18, 2022
#2
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x2-7x=38

Solve the equation for x by finding a, b, and c to plug into the quadratic formula.

All equations of the form ax2+bx+c = 0 can be solved using the quadratic equation! :D It will give two solutions, one being negative and the other being positive. Let's solve!

x2-7x=38

Subtract 38 from both sides

x2-7x -38 = 0

This looks like the ax2+bx+c = 0 formula. A, b, and c are 1, -7, and -38. plug them into the quadratic formula

$$x = {-(-7) \pm \sqrt{7^2-4*1*(-38)} \over 2(1)}$$

simplify to get $$x = {7 \pm \sqrt{201} \over 2}$$

separate into two equations, since quadratic equations always have 2 answers--one positive and one negative

Answer 1: $$x = {7 + \sqrt{201} \over 2}$$

Answer 2:  $$x = {7 - \sqrt{201} \over 2}$$

Jan 18, 2022