x^2+30x-10=0

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Solution for x^2+30x-10=0 equation:


Simplifying
x2 + 30x + -10 = 0

Reorder the terms:
-10 + 30x + x2 = 0

Solving
-10 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 30x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 30x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 30x + x2 = 0 + 10
30x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
30x + x2 = 10

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 = 10 + 225

Reorder the terms:
225 + 30x + x2 = 10 + 225

Combine like terms: 10 + 225 = 235
225 + 30x + x2 = 235

Factor a perfect square on the left side:
(x + 15)(x + 15) = 235

Calculate the square root of the right side: 15.329709717

Break this problem into two subproblems by setting 
(x + 15) equal to 15.329709717 and -15.329709717.

Subproblem 1

x + 15 = 15.329709717 Simplifying x + 15 = 15.329709717 Reorder the terms: 15 + x = 15.329709717 Solving 15 + x = 15.329709717 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 = 15.329709717 + -15 Combine like terms: 15 + -15 = 0 0 + x = 15.329709717 + -15 x = 15.329709717 + -15 Combine like terms: 15.329709717 + -15 = 0.329709717 x = 0.329709717 Simplifying x = 0.329709717

Subproblem 2

x + 15 = -15.329709717 Simplifying x + 15 = -15.329709717 Reorder the terms: 15 + x = -15.329709717 Solving 15 + x = -15.329709717 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 = -15.329709717 + -15 Combine like terms: 15 + -15 = 0 0 + x = -15.329709717 + -15 x = -15.329709717 + -15 Combine like terms: -15.329709717 + -15 = -30.329709717 x = -30.329709717 Simplifying x = -30.329709717

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.329709717, -30.329709717}

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