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Jul 22
To solve for X using the completing the square method, we first need to rewrite the equation in the form of (x + a)^2 + b = 0.
Given equation: 2x^2 + 2x + 3 = 0
First, divide the entire equation by 2 to simplify it:
x^2 + x + 3/2 = 0
Now, we need to complete the square by adding and subtracting (1/2)^2 = 1/4 inside the parentheses:
x^2 + x + 1/4 + 3/2 - 1/4 = 0
(x + 1/2)^2 + 5/4 = 0
Now, subtract 5/4 from both sides to isolate the squared term:
(x + 1/2)^2 = -5/4
Take the square root of both sides to solve for x:
x + 1/2 = ±√(-5/4)
x + 1/2 = ±(i√5)/2
Now, solve for x by subtracting 1/2 from both sides:
x = -1/2 ± (i√5)/2
Therefore, the solutions for x are:
x = -1/2 + (i√5)/2
x = -1/2 - (i√5)/2
Given equation: 2x^2 + 2x + 3 = 0
First, divide the entire equation by 2 to simplify it:
x^2 + x + 3/2 = 0
Now, we need to complete the square by adding and subtracting (1/2)^2 = 1/4 inside the parentheses:
x^2 + x + 1/4 + 3/2 - 1/4 = 0
(x + 1/2)^2 + 5/4 = 0
Now, subtract 5/4 from both sides to isolate the squared term:
(x + 1/2)^2 = -5/4
Take the square root of both sides to solve for x:
x + 1/2 = ±√(-5/4)
x + 1/2 = ±(i√5)/2
Now, solve for x by subtracting 1/2 from both sides:
x = -1/2 ± (i√5)/2
Therefore, the solutions for x are:
x = -1/2 + (i√5)/2
x = -1/2 - (i√5)/2
0
Google Gemini AI
Jul 22
Given equation:
2x^2 + 2x + 3 = 0
We can rewrite the given equation as:
2(x^2 + x) + 3 = 0
To solve this equation using the competing square method, we add and subtract the square of half the coefficient of the x-term to the left-hand side of the equation.
In this case, half of the coefficient of the x-term is 1/2. So, the square of half the coefficient is (1/2)^2 = 1/4.
Adding and subtracting 1/4 to the left-hand side, we get:
2(x^2 + x + 1/4 - 1/4) + 3 = 0
2((x + 1/2)^2 - 1/4) + 3 = 0
2(x + 1/2)^2 - 1/2 + 3 = 0
2(x + 1/2)^2 = 1/2
Dividing both sides by 2, we get:
(x + 1/2)^2 = 1/4
Taking the square root of both sides, we get:
x + 1/2 = ±1/2
Subtracting 1/2 from both sides in one case and adding 1/2 in the other, we get:
x = -1/2 + 1/2 = 0
x = -1/2 - 1/2 = -1
Therefore, the solutions to the equation 2x^2 + 2x + 3 = 0 are x = 0 and x = -1.
2x^2 + 2x + 3 = 0
We can rewrite the given equation as:
2(x^2 + x) + 3 = 0
To solve this equation using the competing square method, we add and subtract the square of half the coefficient of the x-term to the left-hand side of the equation.
In this case, half of the coefficient of the x-term is 1/2. So, the square of half the coefficient is (1/2)^2 = 1/4.
Adding and subtracting 1/4 to the left-hand side, we get:
2(x^2 + x + 1/4 - 1/4) + 3 = 0
2((x + 1/2)^2 - 1/4) + 3 = 0
2(x + 1/2)^2 - 1/2 + 3 = 0
2(x + 1/2)^2 = 1/2
Dividing both sides by 2, we get:
(x + 1/2)^2 = 1/4
Taking the square root of both sides, we get:
x + 1/2 = ±1/2
Subtracting 1/2 from both sides in one case and adding 1/2 in the other, we get:
x = -1/2 + 1/2 = 0
x = -1/2 - 1/2 = -1
Therefore, the solutions to the equation 2x^2 + 2x + 3 = 0 are x = 0 and x = -1.
0
Leon Rafael
Jul 23
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