d^2-30d+7=0

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Solution for d^2-30d+7=0 equation:


Simplifying
d2 + -30d + 7 = 0

Reorder the terms:
7 + -30d + d2 = 0

Solving
7 + -30d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -30d + -7 + d2 = 0 + -7

Reorder the terms:
7 + -7 + -30d + d2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -30d + d2 = 0 + -7
-30d + d2 = 0 + -7

Combine like terms: 0 + -7 = -7
-30d + d2 = -7

The d term is -30d.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30d + 225 + d2 = -7 + 225

Reorder the terms:
225 + -30d + d2 = -7 + 225

Combine like terms: -7 + 225 = 218
225 + -30d + d2 = 218

Factor a perfect square on the left side:
(d + -15)(d + -15) = 218

Calculate the square root of the right side: 14.76482306

Break this problem into two subproblems by setting 
(d + -15) equal to 14.76482306 and -14.76482306.

Subproblem 1

d + -15 = 14.76482306 Simplifying d + -15 = 14.76482306 Reorder the terms: -15 + d = 14.76482306 Solving -15 + d = 14.76482306 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + d = 14.76482306 + 15 Combine like terms: -15 + 15 = 0 0 + d = 14.76482306 + 15 d = 14.76482306 + 15 Combine like terms: 14.76482306 + 15 = 29.76482306 d = 29.76482306 Simplifying d = 29.76482306

Subproblem 2

d + -15 = -14.76482306 Simplifying d + -15 = -14.76482306 Reorder the terms: -15 + d = -14.76482306 Solving -15 + d = -14.76482306 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + d = -14.76482306 + 15 Combine like terms: -15 + 15 = 0 0 + d = -14.76482306 + 15 d = -14.76482306 + 15 Combine like terms: -14.76482306 + 15 = 0.23517694 d = 0.23517694 Simplifying d = 0.23517694

Solution

The solution to the problem is based on the solutions from the subproblems. d = {29.76482306, 0.23517694}

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