round to the nearest hundredth. solve by completing the square.
x^2+10x=18
To complete the square, we need to add and subtract the square of half of the coefficient of x:
x^2 + 10x = 18
x^2 + 10x + 25 - 25 = 18
(x + 5)^2 - 25 = 18
(x + 5)^2 = 43
x + 5 = ±√43
x = -5 ± √43
Now we can round to the nearest hundredth:
x ≈ -5 + 6.56 ≈ 1.56
or
x ≈ -5 - 6.56 ≈ -11.56
Therefore, the solutions rounded to the nearest hundredth are x ≈ 1.56 and x ≈ -11.56.
To complete the square, we need to add and subtract the square of half of the coefficient of x:
x^2 + 10x = 18
x^2 + 10x + 25 - 25 = 18
(x + 5)^2 - 25 = 18
(x + 5)^2 = 43
x + 5 = ±√43
x = -5 ± √43
Now we can round to the nearest hundredth:
x ≈ -5 + 6.56 ≈ 1.56
or
x ≈ -5 - 6.56 ≈ -11.56
Therefore, the solutions rounded to the nearest hundredth are x ≈ 1.56 and x ≈ -11.56.
That's correct! Good job!
To round to the nearest hundredth, we need to first solve the equation by completing the square.
Step 1: Move the constant term to the right side of the equation.
x^2 + 10x - 18 = 0
Step 2: Divide the coefficient of the x-term by 2, square it, and add the result to both sides of the equation.
x^2 + 10x + (10/2)^2 = 18 + (10/2)^2
x^2 + 10x + 25 = 18 + 25
x^2 + 10x + 25 = 43
Step 3: Rewrite the left side of the equation as a perfect square trinomial.
(x + 5)^2 = 43
Step 4: Take the square root of both sides, considering both positive and negative square roots.
x + 5 = ±√43
Step 5: Solve for x by subtracting 5 from both sides of the equation.
x = -5 ± √43
Now, to round to the nearest hundredth, we need to evaluate the approximate values of -5 ± √43.
Using a calculator or a computational tool, we get the approximations:
x ≈ -7.54 or x ≈ 2.54
Therefore, the rounded solutions to the nearest hundredth are x ≈ -7.54 and x ≈ 2.54.