can you help me to solve for completing the squar x^2+18x=-4
x^2 + 18x = -4
take half of the 18, square it, then add to both sides
x^2 + 18x + 81 =-4 + 81
(x+9)^2 = 77
x+9 = ±√77
x = -9 ± √77
Of course! I can help you with that.
Step 1: Move the constant term to the right side of the equation:
x^2 + 18x = -4
x^2 + 18x + 4 = 0
Step 2: Take half of the coefficient of x (which is 18) and square it:
(18/2)^2 = 9^2 = 81
Step 3: Add the result from step 2 to both sides of the equation:
x^2 + 18x + 81 + 4 = 81 + 4
x^2 + 18x + 85 = 85
Step 4: Factor the left side of the equation:
(x + 9)(x + 9) = 85
Step 5: Take the square root of both sides of the equation:
√[(x + 9)(x + 9)] = √85
Step 6: Simplify the square root:
x + 9 = ±√85
Step 7: Solve for x by subtracting 9 from both sides:
x = -9 ±√85
So, the solutions for the equation x^2 + 18x = -4 after completing the square are x = -9 + √85 and x = -9 - √85.
Certainly! To complete the square for the given quadratic equation x^2 + 18x = -4, follow these steps:
Step 1: Move the constant term to the other side of the equation:
x^2 + 18x + 4 = 0
Step 2: Take half of the coefficient of x (which is 18 in this case) and square it. Then add this result to both sides of the equation. This completes the square on the left side of the equation.
x^2 + 18x + (18/2)^2 = -4 + (18/2)^2
Simplifying this:
x^2 + 18x + 81 = -4 + 81
Which becomes:
x^2 + 18x + 81 = 77
Step 3: Rewrite the left side of the equation as a squared binomial. To do this, factor the perfect square trinomial (x^2 + 18x + 81) as (x + 9)^2.
(x + 9)^2 = 77
Step 4: Take the square root of both sides of the equation.
√((x + 9)^2) = ±√77
Simplifying this:
x + 9 = ±√77
Step 5: Finally, solve for x by subtracting 9 from both sides of the equation.
x = -9 ± √77
So, the solutions to the quadratic equation x^2 + 18x = -4, after completing the square, are x = -9 + √77 and x = -9 - √77.