Solve the equation by completing the square. Round to the nearest hundredth. x^2+6x=-7
First, we need to move the constant to the other side:
x^2 + 6x + 7 = 0
Next, we need to complete the square. To do this, we take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 + 6x + 9 = 2
The left side can be factored as a perfect square:
(x + 3)^2 = 2
Taking the square root of both sides:
x + 3 = ± √2
Subtracting 3 from both sides:
x = -3 ± √2
Rounding to the nearest hundredth:
x ≈ -3.41, -0.59
Solve the equation by completing the square. Round to the nearest hundredth.
x^2+6x=-7
First, we need to move the constant to the other side:
x^2 + 6x + 7 = 0
Next, we need to complete the square. To do this, we take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 + 6x + 9 = 2
The left side can be factored as a perfect square:
(x + 3)^2 = 2
Taking the square root of both sides:
x + 3 = ± √2
Subtracting 3 from both sides:
x = -3 ± √2
Rounding to the nearest hundredth:
x ≈ -3.41, -0.59
Solve the equation by completing the square. Round to the nearest hundredth.
x^2-6x=-7
First, we need to move the constant to the other side:
x^2 - 6x + 7 = 0
Next, we need to complete the square. To do this, we take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 - 6x + 9 = 2
The left side can be factored as a perfect square:
(x - 3)^2 = 2
Taking the square root of both sides:
x - 3 = ± √2
Subtracting 3 from both sides:
x = 3 ± √2
Rounding to the nearest hundredth:
x ≈ 4.41, 1.59
Solve the equation by completing the square.
x^2-6x+7=0
To complete the square, we need to add and subtract the square of half the coefficient of x:
x^2 - 6x + (9 - 9) + 7 = 0
The first three terms can be factored as a perfect square:
(x - 3)^2 - 2 = 0
Adding 2 to both sides:
(x - 3)^2 = 2
Taking the square root of both sides:
x - 3 = ± √2
Adding 3 to both sides:
x = 3 ± √2
Therefore, the solution is x = 3 ± √2.
Solve the equation by completing the square. x^2-6x+7=0
To complete the square, we need to add and subtract the square of half the coefficient of x:
x^2 - 6x + (9 - 9) + 7 = 0
The first three terms can be factored as a perfect square:
(x - 3)^2 - 2 = 0
Adding 2 to both sides:
(x - 3)^2 = 2
Taking the square root of both sides:
x - 3 = ± √2
Adding 3 to both sides:
x = 3 ± √2
Therefore, the solution is x = 3 ± √2.