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Sagot :
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
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