Respuesta :
ANSWER
[tex]x = - 11\: or \: x = 3[/tex]
EXPLANATION
The quadratic equation given to us is
[tex] {x}^{2} + 8x = 33[/tex]
We add half the square of the coefficient of
[tex]x[/tex]
to both sides of the equation to obtain,
[tex] {x}^{2} + 8x + {(4)}^{2} = 33 + {(4)}^{2}[/tex]
This implies that,
[tex] {x}^{2} + 8x + {(4)}^{2} = 33 + 16[/tex]
The right hand side simplifies to
[tex] {x}^{2} + 8x + {(4)}^{2} = 49[/tex]
The left hand side is a perfect square.
This gives us
[tex] {(x + 4)}^{2} = 49[/tex]
We take the square root of both sides
[tex]x + 4 = \pm \sqrt{49} [/tex]
This evaluates to
[tex]x + 4 = \pm 7[/tex]
We make x the subject.
[tex]x = - 4\pm 7[/tex]
We now split the square root sign to get
.
[tex]x = - 4 - 7 \: or \: x = - 4 + 7[/tex]
[tex]x = - 11\: or \: x = 3[/tex]
The correct answer is A.
[tex]x = - 11\: or \: x = 3[/tex]
EXPLANATION
The quadratic equation given to us is
[tex] {x}^{2} + 8x = 33[/tex]
We add half the square of the coefficient of
[tex]x[/tex]
to both sides of the equation to obtain,
[tex] {x}^{2} + 8x + {(4)}^{2} = 33 + {(4)}^{2}[/tex]
This implies that,
[tex] {x}^{2} + 8x + {(4)}^{2} = 33 + 16[/tex]
The right hand side simplifies to
[tex] {x}^{2} + 8x + {(4)}^{2} = 49[/tex]
The left hand side is a perfect square.
This gives us
[tex] {(x + 4)}^{2} = 49[/tex]
We take the square root of both sides
[tex]x + 4 = \pm \sqrt{49} [/tex]
This evaluates to
[tex]x + 4 = \pm 7[/tex]
We make x the subject.
[tex]x = - 4\pm 7[/tex]
We now split the square root sign to get
.
[tex]x = - 4 - 7 \: or \: x = - 4 + 7[/tex]
[tex]x = - 11\: or \: x = 3[/tex]
The correct answer is A.
The polynomial x^2 + 8x = 33 by completing the square of the solution set of equation -11.
The quadratic equation given to us is
[tex]x^2+8x=33[/tex]
What is the complete square method?
The Completing Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial.
We add half the square of the coefficient of x to both sides of the equation to obtain,
[tex]x^2+8x+4^2=33+4^2[/tex]
This implies that,
[tex]x^2+8x+4^2=33+16[/tex]
This implies that,
[tex]x^2+8x+4^2=49[/tex]
The right-hand side simplifies to
This gives us
[tex](x+4)^2=49[/tex]
We take the square root of both sides
The left-hand side is a perfect square.
This evaluates to
We take the square root of both sides
[tex](x+4)= \±\sqrt{49}[/tex]
We now split the square root sign to get
[tex]x+4=\±7[/tex]
[tex]x=-4-7 or x=-4+7[/tex]
[tex]x=-11 or x=3[/tex]
The correct answer is A.
The polynomial x^2 + 8x = 33 by completing the square the solution set of equation -11.
To learn more about the solution set visit:
https://brainly.com/question/12249971
