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Radda [10]
3 years ago
6

Complete the steps for solving 7 = –2x2 + 10x.

Mathematics
1 answer:
frutty [35]3 years ago
8 0

Answer:

<em>x = ( √11 + 5 ) / 2, and x = ( - √11 + 5 ) / 2</em>

Step-by-step explanation:

Let us solve by completing the square;

7 = - 2x^2 + 10x, ⇒ Switch sides,

- 2x^2 + 10x = 7, ⇒ Divide both sides by - 2,

x^2 - 5x = - 7 / 2, ⇒ Write the equation in the form x^2 + 2ax+ a^2, ( x + a )^2, solving for the value of a,

2ax = - 5x,

a = - 5x / 2x,

a = - 5 / 2, ⇒ Add a^2 ⇒ ( - 5 / 2 )^2 to either side of equation,

x^2 - 5x +  ( - 5 / 2 )^2 = - 7 / 2 + ( - 5 / 2 )^2, ⇒ Simplify,

( x - 5 / 2 )^2 = 11 / 4,

| x - 5 / 2 | = √ ( 11 / 4 ), Solve for value( s ) of x,

<em>Answer; x = ( √11 + 5 ) / 2, and x = ( - √11 + 5 ) / 2</em>

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<em>Alternate solution</em>

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<em>Comment on other alternate solutions</em>

There are many other ways you can find the area of this figure. It can be divided into rectangles, triangles, or other figures of your choice. The appropriate area formulas should be used, and the resulting partial areas added or subtracted as required.

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