x^2-30x-1458.074=0

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Solution for x^2-30x-1458.074=0 equation:


Simplifying
x2 + -30x + -1458.074 = 0

Reorder the terms:
-1458.074 + -30x + x2 = 0

Solving
-1458.074 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1458.074' to each side of the equation.
-1458.074 + -30x + 1458.074 + x2 = 0 + 1458.074

Reorder the terms:
-1458.074 + 1458.074 + -30x + x2 = 0 + 1458.074

Combine like terms: -1458.074 + 1458.074 = 0.000
0.000 + -30x + x2 = 0 + 1458.074
-30x + x2 = 0 + 1458.074

Combine like terms: 0 + 1458.074 = 1458.074
-30x + x2 = 1458.074

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

Add '225' to each side of the equation.
-30x + 225 + x2 = 1458.074 + 225

Reorder the terms:
225 + -30x + x2 = 1458.074 + 225

Combine like terms: 1458.074 + 225 = 1683.074
225 + -30x + x2 = 1683.074

Factor a perfect square on the left side:
(x + -15)(x + -15) = 1683.074

Calculate the square root of the right side: 41.025284886

Break this problem into two subproblems by setting 
(x + -15) equal to 41.025284886 and -41.025284886.

Subproblem 1

x + -15 = 41.025284886 Simplifying x + -15 = 41.025284886 Reorder the terms: -15 + x = 41.025284886 Solving -15 + x = 41.025284886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 41.025284886 + 15 Combine like terms: -15 + 15 = 0 0 + x = 41.025284886 + 15 x = 41.025284886 + 15 Combine like terms: 41.025284886 + 15 = 56.025284886 x = 56.025284886 Simplifying x = 56.025284886

Subproblem 2

x + -15 = -41.025284886 Simplifying x + -15 = -41.025284886 Reorder the terms: -15 + x = -41.025284886 Solving -15 + x = -41.025284886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -41.025284886 + 15 Combine like terms: -15 + 15 = 0 0 + x = -41.025284886 + 15 x = -41.025284886 + 15 Combine like terms: -41.025284886 + 15 = -26.025284886 x = -26.025284886 Simplifying x = -26.025284886

Solution

The solution to the problem is based on the solutions from the subproblems. x = {56.025284886, -26.025284886}

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