Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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}

Sagot :

jcherry99

Answer:

(-12,2)

Step-by-step explanation:

x^2 + 10x = 24

x^2 + 10x + (10/2)^2 = 24 + (10/2)^2

10/2 = 5

5^2 = 25

x^2 + 10x + 25 = 24 + 25

x^2 + 10x + 25 = 49

(x + 5)^2 = 49                 Take the square root of both sides

(x + 5) = sqrt(49)

x + 5 = +/- 7

x = +/- 7 - 5

x = +7 - 5 = 2

x = -7 - 5 = -12

Answer:

{ -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.

[tex] \small \sf \sqrt{(x + 5) {}^{2} } = \sqrt{49} [/tex]

simplify

  • x + 5 = 7
  • x + 5 = +/- 7

Subtract 5 from both sides.

x + 5 - 5 = 7 - 5

  • x = 2

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

  • x = -7 - 5 = -12

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.