0.012x^2+4.2x-30=0

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Solution for 0.012x^2+4.2x-30=0 equation:


Simplifying
0.012x2 + 4.2x + -30 = 0

Reorder the terms:
-30 + 4.2x + 0.012x2 = 0

Solving
-30 + 4.2x + 0.012x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.012'.
-2500 + 350x + x2 = 0

Move the constant term to the right:

Add '2500' to each side of the equation.
-2500 + 350x + 2500 + x2 = 0 + 2500

Reorder the terms:
-2500 + 2500 + 350x + x2 = 0 + 2500

Combine like terms: -2500 + 2500 = 0
0 + 350x + x2 = 0 + 2500
350x + x2 = 0 + 2500

Combine like terms: 0 + 2500 = 2500
350x + x2 = 2500

The x term is 350x.  Take half its coefficient (175).
Square it (30625) and add it to both sides.

Add '30625' to each side of the equation.
350x + 30625 + x2 = 2500 + 30625

Reorder the terms:
30625 + 350x + x2 = 2500 + 30625

Combine like terms: 2500 + 30625 = 33125
30625 + 350x + x2 = 33125

Factor a perfect square on the left side:
(x + 175)(x + 175) = 33125

Calculate the square root of the right side: 182.002747232

Break this problem into two subproblems by setting 
(x + 175) equal to 182.002747232 and -182.002747232.

Subproblem 1

x + 175 = 182.002747232 Simplifying x + 175 = 182.002747232 Reorder the terms: 175 + x = 182.002747232 Solving 175 + x = 182.002747232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-175' to each side of the equation. 175 + -175 + x = 182.002747232 + -175 Combine like terms: 175 + -175 = 0 0 + x = 182.002747232 + -175 x = 182.002747232 + -175 Combine like terms: 182.002747232 + -175 = 7.002747232 x = 7.002747232 Simplifying x = 7.002747232

Subproblem 2

x + 175 = -182.002747232 Simplifying x + 175 = -182.002747232 Reorder the terms: 175 + x = -182.002747232 Solving 175 + x = -182.002747232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-175' to each side of the equation. 175 + -175 + x = -182.002747232 + -175 Combine like terms: 175 + -175 = 0 0 + x = -182.002747232 + -175 x = -182.002747232 + -175 Combine like terms: -182.002747232 + -175 = -357.002747232 x = -357.002747232 Simplifying x = -357.002747232

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.002747232, -357.002747232}

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