-x^2+36x-62=0

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Solution for -x^2+36x-62=0 equation:


Simplifying
-1x2 + 36x + -62 = 0

Reorder the terms:
-62 + 36x + -1x2 = 0

Solving
-62 + 36x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
62 + -36x + x2 = 0

Move the constant term to the right:

Add '-62' to each side of the equation.
62 + -36x + -62 + x2 = 0 + -62

Reorder the terms:
62 + -62 + -36x + x2 = 0 + -62

Combine like terms: 62 + -62 = 0
0 + -36x + x2 = 0 + -62
-36x + x2 = 0 + -62

Combine like terms: 0 + -62 = -62
-36x + x2 = -62

The x term is -36x.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x + 324 + x2 = -62 + 324

Reorder the terms:
324 + -36x + x2 = -62 + 324

Combine like terms: -62 + 324 = 262
324 + -36x + x2 = 262

Factor a perfect square on the left side:
(x + -18)(x + -18) = 262

Calculate the square root of the right side: 16.186414056

Break this problem into two subproblems by setting 
(x + -18) equal to 16.186414056 and -16.186414056.

Subproblem 1

x + -18 = 16.186414056 Simplifying x + -18 = 16.186414056 Reorder the terms: -18 + x = 16.186414056 Solving -18 + x = 16.186414056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 16.186414056 + 18 Combine like terms: -18 + 18 = 0 0 + x = 16.186414056 + 18 x = 16.186414056 + 18 Combine like terms: 16.186414056 + 18 = 34.186414056 x = 34.186414056 Simplifying x = 34.186414056

Subproblem 2

x + -18 = -16.186414056 Simplifying x + -18 = -16.186414056 Reorder the terms: -18 + x = -16.186414056 Solving -18 + x = -16.186414056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -16.186414056 + 18 Combine like terms: -18 + 18 = 0 0 + x = -16.186414056 + 18 x = -16.186414056 + 18 Combine like terms: -16.186414056 + 18 = 1.813585944 x = 1.813585944 Simplifying x = 1.813585944

Solution

The solution to the problem is based on the solutions from the subproblems. x = {34.186414056, 1.813585944}

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