solve the equation giving your answer in correct to 2 decimal places 5x square+4x+1=3(1-3x)
Multiply out the term on the right, combine like terms, and use the quadratic formula (unless you can factor it).
5x^2 +4x +1 = -9x +3
5x^2 -13x -2 = 0
Now solve.
x = (1/10)[13 +/-sqrt(209)]
(a) ( x+1)2 =9
So are you using the quadratic formula?
To solve the equation, we'll start by simplifying both sides and transforming it into a quadratic equation in standard form (ax^2 + bx + c = 0).
Given equation: 5x^2 + 4x + 1 = 3(1 - 3x)
First, distribute 3 on the right side:
5x^2 + 4x + 1 = 3 - 9x
Next, combine like terms on both sides:
5x^2 + 4x + 1 = -9x + 3
Now, move all terms to one side to form a quadratic equation:
5x^2 + 4x + 1 + 9x - 3 = 0
Combine like terms:
5x^2 + 13x - 2 = 0
This is now a quadratic equation in standard form. To solve it, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our quadratic equation, the values of a, b, and c are:
a = 5, b = 13, c = -2
Plugging these values into the quadratic formula, we get:
x = (-13 ± √(13^2 - 4 * 5 * -2)) / (2 * 5)
Simplifying further:
x = (-13 ± √(169 + 40)) / 10
x = (-13 ± √209) / 10
Using a calculator, we can compute the square root of 209, which is approximately 14.4568.
So, the solutions (rounded to 2 decimal places) are:
x = (-13 + 14.4568) / 10 ≈ 1.1457
x = (-13 - 14.4568) / 10 ≈ -2.7457
Therefore, the solutions to the given equation, rounded to 2 decimal places, are approximately:
x ≈ 1.15
x ≈ -2.75