Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+16)^2/9=7 .
To solve the quadratic equation using square roots, first isolate the squared term:
(x+16)^2/9 = 7
Multiply both sides of the equation by 9:
(x+16)^2 = 63
Take the square root of both sides of the equation to solve for x:
√((x+16)^2) = √63
Simplify both sides:
x+16 = ±√63
Now subtract 16 from both sides:
x = -16 ± √63
Rounding to the nearest hundredth:
x ≈ -16 + 7.94 ≈ -8.06
x ≈ -16 - 7.94 ≈ -23.94
Therefore, the solutions to the quadratic equation are x ≈ -8.06 and x ≈ -23.94.
To solve the quadratic equation (x+16)^2/9=7 using square roots, we will isolate x step-by-step.
Step 1: Multiply both sides of the equation by 9 to eliminate the fraction:
9 * (x+16)^2/9 = 7 * 9
(x+16)^2 = 63
Step 2: Take the square root of both sides of the equation:
√((x+16)^2) = √63
Step 3: Simplify the square root on the left side:
|x+16| = √63
Step 4: Set up two equations to account for both positive and negative square roots:
x+16 = √63 or x+16 = -√63
Step 5: Solve for x in each equation:
For x+16 = √63:
x = √63 - 16
For x+16 = -√63:
x = -√63 - 16
Step 6: Calculate the approximate values, rounded to the nearest hundredth, using a calculator:
For x+16 = √63:
x ≈ √63 - 16 ≈ -4.40
For x+16 = -√63:
x ≈ -√63 - 16 ≈ -27.46
So, the two possible solutions for the quadratic equation are x ≈ -4.40 and x ≈ -27.46.
To solve the quadratic equation using square roots, we need to first isolate the variable x.
Here's how to do it step by step:
1. Multiply both sides of the equation by 9 to remove the denominator:
(x + 16)^2 = 63
2. Take the square root of both sides of the equation, remembering to consider both the positive and negative square roots:
√((x + 16)^2) = ±√63
This gives us two separate equations:
x + 16 = ±√63
3. To isolate x, we can subtract 16 from both sides of each equation:
x = -16 ± √63
Now, let's simplify the square root of 63:
√63 ≈ 7.94 (rounded to the nearest hundredth).
Plugging this value into our equations:
x = -16 + 7.94 ≈ -8.06
x = -16 - 7.94 ≈ -23.94
So the solutions to the quadratic equation (x+16)^2/9 = 7 are approximately x ≈ -8.06 and x ≈ -23.94 when rounded to the nearest hundredth.