0=-(x^2-30x+150)

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Solution for 0=-(x^2-30x+150) equation:


Simplifying
0 = -1(x2 + -30x + 150)

Reorder the terms:
0 = -1(150 + -30x + x2)
0 = (150 * -1 + -30x * -1 + x2 * -1)
0 = (-150 + 30x + -1x2)

Solving
0 = -150 + 30x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 150 = 150
150 + -30x + x2 = -150 + 30x + -1x2 + 150 + -30x + x2

Reorder the terms:
150 + -30x + x2 = -150 + 150 + 30x + -30x + -1x2 + x2

Combine like terms: -150 + 150 = 0
150 + -30x + x2 = 0 + 30x + -30x + -1x2 + x2
150 + -30x + x2 = 30x + -30x + -1x2 + x2

Combine like terms: 30x + -30x = 0
150 + -30x + x2 = 0 + -1x2 + x2
150 + -30x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
150 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-150' to each side of the equation.
150 + -30x + -150 + x2 = 0 + -150

Reorder the terms:
150 + -150 + -30x + x2 = 0 + -150

Combine like terms: 150 + -150 = 0
0 + -30x + x2 = 0 + -150
-30x + x2 = 0 + -150

Combine like terms: 0 + -150 = -150
-30x + x2 = -150

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 = -150 + 225

Reorder the terms:
225 + -30x + x2 = -150 + 225

Combine like terms: -150 + 225 = 75
225 + -30x + x2 = 75

Factor a perfect square on the left side:
(x + -15)(x + -15) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + -15) equal to 8.660254038 and -8.660254038.

Subproblem 1

x + -15 = 8.660254038 Simplifying x + -15 = 8.660254038 Reorder the terms: -15 + x = 8.660254038 Solving -15 + x = 8.660254038 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 = 8.660254038 + 15 Combine like terms: -15 + 15 = 0 0 + x = 8.660254038 + 15 x = 8.660254038 + 15 Combine like terms: 8.660254038 + 15 = 23.660254038 x = 23.660254038 Simplifying x = 23.660254038

Subproblem 2

x + -15 = -8.660254038 Simplifying x + -15 = -8.660254038 Reorder the terms: -15 + x = -8.660254038 Solving -15 + x = -8.660254038 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 = -8.660254038 + 15 Combine like terms: -15 + 15 = 0 0 + x = -8.660254038 + 15 x = -8.660254038 + 15 Combine like terms: -8.660254038 + 15 = 6.339745962 x = 6.339745962 Simplifying x = 6.339745962

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.660254038, 6.339745962}

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