Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation? (negative 5 minus StartRoot 34 EndRoot comma negative 5 + Startroot 34 EndRoot)
(negative 5 minus StartRoot 29 EndRoot comma negative 5 + StartRoot 29 EndRoot)
{–12, 2}
{–2, 12}

{ -12 , 2}

Step-by-step explanation:

x² + 10x = 24

In order to complete the square, the equation must first be in the form x² + bx =c.

x² + 10x = 24

Divide 10, the coefficient of the x term, by 2 to get 5. Then add the square of 5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

x² + 10x + 5² = 24 + 5²

expand exponents.

x² + 10x + 25 = 24 + 25

Add 24 and 25

x² + 10x + 25 = 49

Factor x² + 10x + 25. In general, when x² + bx + c is a perfect square, it can always be factored as ( x + b/2)².

( x + 5 )² =49

Take the square root of both sides of the equation.

simplify

x + 5 = 7x + 5 = +/- 7

Subtract 5 from both sides.

x + 5 - 5 = 7 - 5

x = 2

x + 5 - 5 = +/- 7 -5

x = -7 - 5 = -12

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so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.