To solve this equation, we need to first simplify the left side of the equation.Given equation:3x² + 1 = 2x * (x + 1)
Expanding the expression on the right side:3x² + 1 = 2x² + 2x
Now, bring all terms to one side of the equation:3x² - 2x² + 2x - 1 = 0x² + 2x - 1 = 0
Now, we have a quadratic equation in the form of ax² + bx + c = 0.To solve this, we can use the quadratic formula:x = [-b ± √(b² - 4ac)] / 2a
In our case:a = 1, b = 2, c = -1
Plugging in the values:x = [-2 ± √(2² - 41(-1))] / 2*1x = [-2 ± √(4 + 4)] / 2x = [-2 ± √8] / 2x = (-2 ± 2√2) / 2x = -1 ± √2
So, the solutions to the equation are:x = -1 + √2 and x = -1 - √2
To solve this equation, we need to first simplify the left side of the equation.
Given equation:
3x² + 1 = 2x * (x + 1)
Expanding the expression on the right side:
3x² + 1 = 2x² + 2x
Now, bring all terms to one side of the equation:
3x² - 2x² + 2x - 1 = 0
x² + 2x - 1 = 0
Now, we have a quadratic equation in the form of ax² + bx + c = 0.
To solve this, we can use the quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a
In our case:
a = 1, b = 2, c = -1
Plugging in the values:
x = [-2 ± √(2² - 41(-1))] / 2*1
x = [-2 ± √(4 + 4)] / 2
x = [-2 ± √8] / 2
x = (-2 ± 2√2) / 2
x = -1 ± √2
So, the solutions to the equation are:
x = -1 + √2 and x = -1 - √2