Math

Question Find the square root of (d3)2+25=0(d-3)^{2}+25=0 to get the values of dd.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation (d3)2+25=0(d-3)^{2}+25=0.
2. We need to solve for the variable dd using the square root method.
3. The square root method involves isolating the squared term and taking the square root of both sides of the equation.

STEP 2

Isolate the squared term by subtracting 25 from both sides of the equation.
(d3)2+2525=025(d-3)^{2}+25-25=0-25

STEP 3

Simplify the equation.
(d3)2=25(d-3)^{2}=-25

STEP 4

Take the square root of both sides of the equation to solve for d3d-3. Remember that taking the square root of a negative number introduces the imaginary unit ii, where i2=1i^2 = -1.
(d3)2=25\sqrt{(d-3)^{2}}=\sqrt{-25}

STEP 5

Simplify the left side of the equation by removing the square root and the square, and simplify the right side by factoring out ii.
d3=±5id-3=\pm 5i

STEP 6

Add 3 to both sides of the equation to solve for dd.
d3+3=±5i+3d-3+3=\pm 5i + 3

STEP 7

Simplify the equation to find the values of dd.
d=3±5id=3 \pm 5i
The values of the variable dd that would make the statement true are d=3+5id=3 + 5i and d=35id=3 - 5i.
The correct answer is d) d=3±5id=3 \pm 5i.

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