solve for x:3x2+2x+6=10(correct to two decimal digits)
Online "^" indicates an exponent.
Subtract 10 from both sides.
3x^2 + 2x - 4 = 0
Factor.
(3x-2)(x+2)= 0
I hope you can take it from here.
y=a*x^2+b*x+c
3*x^2+2*x+6=10
3*x^2+2*x+6=10
3*x^2+2*x+6-10=0
3*x^2+2*x-4=0
a=3 , b=2 , c=-4
x1=(-b-sqroot(b^2-4*a*c))/(2*a)
x1=(-2-sqroot(2^2-4*3*(-4)/(2*3)
=(-2-sqroot(4+48)/6
=(-2-sqroot(52))/6=
=(-2-sqroot(4*13))/6
=(-2-2*sqroot(13))/6
=(-2/6)*((1+sqroot(13))
=(-1/3)*(1+3.60555)
=(-1/3)*4.6055
=-1.535166
x1=-1.54
x2
x2=(-b+sqroot(b^2-4*a*c))/(2*a)
x2=(-2+sqroot(2^2-4*3*(-4)/(2*3)
=(-2+sqroot(4+48)/6
=(-2+sqroot(52))/6=
=(-2-sqroot(4*13))/6
=(-2+2*sqroot(13))/6
=(-2/6)*(1-sqroot(13))
=(-1/3)*(1-3.60555)
=(-1/3)*(-2.60555)
=0.868516
x2=0.87
To solve the equation 3x^2 + 2x + 6 = 10, you need to find the value of x that makes the equation true. Here's how you can solve it step-by-step:
1. Start by subtracting 10 from both sides of the equation to isolate the quadratic term:
3x^2 + 2x + 6 - 10 = 10 - 10
3x^2 + 2x - 4 = 0
2. Rewrite the equation in the standard form of a quadratic equation:
3x^2 + 2x - 4 = 0
3. To solve this quadratic equation, you can use the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. In this equation, a, b, and c are the coefficients of the quadratic equation.
For our equation 3x^2 + 2x - 4 = 0, a = 3, b = 2, and c = -4.
4. Now, plug the values of a, b, and c into the quadratic formula and calculate the two possible solutions for x:
x = (-2 ± √(2^2 - 4 * 3 * -4)) / (2 * 3)
x = (-2 ± √(4 + 48)) / 6
x = (-2 ± √52) / 6
x = (-2 ± 2√13) / 6
5. Simplify the expression by dividing both the numerator and denominator by 2:
x = -1/3 ± √13/3
6. To get the two decimal digit approximation, you can use a calculator to evaluate the expression:
x ≈ -1.39 or x ≈ 0.39
Therefore, the solutions to the equation 3x^2 + 2x + 6 = 10, correct to two decimal digits, are x ≈ -1.39 and x ≈ 0.39.