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ser-zykov [4K]
2 years ago
5

Solve the equation for all values of x by completing the square. 5x^2-70x=-230

Mathematics
2 answers:
elena-s [515]2 years ago
7 0

\sf x=\pm \sqrt{3}+7

solving step wise:

\sf 5x^2-70x=-230

<u>divide the following by 5</u>

\sf x^2-14x=-46

<u>completing square</u>

<u />\sf (x-\dfrac{14}{2})^2-(\dfrac{14}{2})^2   =-46

<u>should look like this</u>

\sf (x-7)^2-49=-46

<u>simplify by changing sides</u>

\sf x-7=\pm \sqrt{3}

<u><em>final answer:</em></u>

\sf x=\pm \sqrt{3}+7

Elina [12.6K]2 years ago
4 0

Answer:

x=7 + \sqrt{3}

x=7 - \sqrt{3}

Step-by-step explanation:

Given equation:

5x^2-70x=-230

Divide both sides by 5:

x^2-14x=-46

Square half of the coefficient of x:  (-14 \div 2)^2=49
and add this to both sides:

x^2-14x+49=-46+49

Factor the left side and simplify the right side:

(x-7)^2=3

Square root both sides:

x-7=\pm\sqrt{3}

Add 7 to both sides:

x=7 \pm \sqrt{3}

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The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

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a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

Will have a characteristic equation of the form:

a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0

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For real repeated roots the solution is given by:

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For complex roots the solution is given by:

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x=-cos(t)+2sin(t)

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