Use square roots to solve these equations. Round to the nearest hundredth if necessary.
5x^2 + 536 = 651.
Also,problem 2: 3z^2 + 52 = -56
5 x^2 = 651-536 = 115
x^2 = 23
x = +/- sqrt 23 = +/- 4.80
3 z^2 = -108
z^2 = -36
z = +/-6 sqrt -1
= +/- 6i
To solve the given equations using square roots, we need to isolate the variable (x or z) first. Then we can apply the square root operation to both sides of the equation.
Problem 1: 5x^2 + 536 = 651
Step 1: Subtract 536 from both sides of the equation to isolate the variable.
5x^2 = 651 - 536
5x^2 = 115
Step 2: Divide both sides of the equation by 5 to solve for x^2.
x^2 = 115/5
x^2 = 23
Step 3: Apply the square root operation to both sides to solve for x.
√(x^2) = √23
x = ± √23
Therefore, the solutions to the equation are x = ± √23.
Problem 2: 3z^2 + 52 = -56
Step 1: Subtract 52 from both sides of the equation to isolate the variable.
3z^2 = -56 - 52
3z^2 = -108
Step 2: Divide both sides of the equation by 3 to solve for z^2.
z^2 = -108/3
z^2 = -36
Step 3: Apply the square root operation to both sides to solve for z.
√(z^2) = √(-36)
z = ± √(-36)
The square root of a negative number is not a real number. Therefore, this equation has no real solutions.
In summary, the solution to the first equation is x = ± √23, and the second equation has no real solutions.