4x^2+30x-75=0

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Solution for 4x^2+30x-75=0 equation:


Simplifying
4x2 + 30x + -75 = 0

Reorder the terms:
-75 + 30x + 4x2 = 0

Solving
-75 + 30x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-18.75 + 7.5x + x2 = 0

Move the constant term to the right:

Add '18.75' to each side of the equation.
-18.75 + 7.5x + 18.75 + x2 = 0 + 18.75

Reorder the terms:
-18.75 + 18.75 + 7.5x + x2 = 0 + 18.75

Combine like terms: -18.75 + 18.75 = 0.00
0.00 + 7.5x + x2 = 0 + 18.75
7.5x + x2 = 0 + 18.75

Combine like terms: 0 + 18.75 = 18.75
7.5x + x2 = 18.75

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 18.75 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 18.75 + 14.0625

Combine like terms: 18.75 + 14.0625 = 32.8125
14.0625 + 7.5x + x2 = 32.8125

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 32.8125

Calculate the square root of the right side: 5.728219619

Break this problem into two subproblems by setting 
(x + 3.75) equal to 5.728219619 and -5.728219619.

Subproblem 1

x + 3.75 = 5.728219619 Simplifying x + 3.75 = 5.728219619 Reorder the terms: 3.75 + x = 5.728219619 Solving 3.75 + x = 5.728219619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 5.728219619 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 5.728219619 + -3.75 x = 5.728219619 + -3.75 Combine like terms: 5.728219619 + -3.75 = 1.978219619 x = 1.978219619 Simplifying x = 1.978219619

Subproblem 2

x + 3.75 = -5.728219619 Simplifying x + 3.75 = -5.728219619 Reorder the terms: 3.75 + x = -5.728219619 Solving 3.75 + x = -5.728219619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -5.728219619 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -5.728219619 + -3.75 x = -5.728219619 + -3.75 Combine like terms: -5.728219619 + -3.75 = -9.478219619 x = -9.478219619 Simplifying x = -9.478219619

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.978219619, -9.478219619}

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