Solve.
10x^2+5x=-5
Is this a great start: 10x^2+5x=-5
+5 +5
10x^2+5x+5=0
10(x+5)(x+1)=0
10=0 x=5 x=-1
we are still ok with
10x^2+5x+5=0
now divide each term by 5
2x^2 + x + 1 = 0
doesn't factor, so we have to use the formula
x = (-1 ± √(1 - 4(2)(1)) )/4
= (-1 ± √-7)/4
= (-1 ± √7 i)/4 , a pair of complex numbers
To solve the equation 10x^2 + 5x = -5, we can follow these steps:
Step 1: Arrange the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, we have 10x^2 + 5x + 5 = 0.
Step 2: Apply the quadratic formula, which states that x = (-b ± √(b^2 - 4ac)) / (2a). For our equation, a = 10, b = 5, and c = 5.
Substituting these values into the quadratic formula, we get:
x = (-(5) ± √((5)^2 - 4(10)(5))) / (2(10))
x = (-5 ± √(25 - 200)) / 20
x = (-5 ± √(-175)) / 20
Step 3: Simplify the square root expression. Since the square root of a negative number is not a real number, we can't find the exact solution for x. However, we can express it using imaginary numbers.
√(-175) = √(175) * i, where i is the imaginary unit (√(-1)).
Step 4: Substitute the simplified square root back into the equation:
x = (-5 ± √(175) * i) / 20
This is the solution to the equation 10x^2 + 5x = -5. It cannot be simplified any further without knowing the value of √(175).