which expression gives the solutions of -5+2x^2=-6x
no idea, but the equation can be written as
2x^2+6x-5 = 0
so solve in the usual ways.
which expression gives the solutions of -5+2x^2=-6x
2+-\sqrt(4-(4)(6)(-5))
over 12
-5+-\sqrt(25-(4)(2)(6)
over -10
-6+-\sqrt(36-(4)(2)(-5))
over 4
6+-\sqrt(36-(4)(2)(-5))
over 4
To find the solutions of the equation -5 + 2x^2 = -6x, we need to rearrange the equation to isolate the variable x.
Step 1: Move all the terms to one side of the equation to get a quadratic equation.
-5 + 2x^2 + 6x = 0
Step 2: Rearrange the equation in standard quadratic form (ax^2 + bx + c = 0).
2x^2 + 6x - 5 = 0
Step 3: Use factoring, completing the square, or the quadratic formula to solve the equation.
In this case, factoring may not be straightforward, so let's solve it using the quadratic formula.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c correspond to the coefficients in the quadratic equation ax^2 + bx + c = 0.
For our equation (2x^2 + 6x - 5 = 0), we have:
a = 2,
b = 6, and
c = -5.
Substituting these values into the quadratic formula, we get:
x = (-6 ± √(6^2 - 4(2)(-5))) / (2(2))
x = (-6 ± √(36 + 40)) / 4
x = (-6 ± √76) / 4
x = (-6 ± √(4 * 19)) / 4
x = (-6 ± 2√19) / 4
Step 4: Simplify the expression.
x = (-3 ± √19) / 2
Therefore, the expression that gives the solutions for -5 + 2x^2 = -6x is:
x = (-3 ± √19) / 2
To find the solutions of the equation -5 + 2x^2 = -6x, we need to rearrange the equation into the form of a quadratic equation (ax^2 + bx + c = 0).
1. Move all the terms to one side of the equation:
-5 + 2x^2 + 6x = 0
2. Rearrange the terms in descending order of x^2:
2x^2 + 6x - 5 = 0
The expression that gives the solutions of this equation is the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, we can substitute a = 2, b = 6, and c = -5 into the quadratic formula to get the solutions.
x = (-6 ± √(6^2 - 4(2)(-5))) / (2(2))
Simplifying further:
x = (-6 ± √(36 + 40)) / 4
x = (-6 ± √(76)) / 4
x = (-6 ± √(4 * 19)) / 4
x = (-6 ± 2√19) / 4
Finally, we can simplify the expression further:
x = (-3 ± √19) / 2
So, the solutions of the equation -5 + 2x^2 = -6x are given by the expression (-3 ± √19) / 2.