1500x^2+212058x-11133045=0

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Solution for 1500x^2+212058x-11133045=0 equation:


Simplifying
1500x2 + 212058x + -11133045 = 0

Reorder the terms:
-11133045 + 212058x + 1500x2 = 0

Solving
-11133045 + 212058x + 1500x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3711015 + 70686x + 500x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-3711015 + 70686x + 500x2)' equal to zero and attempt to solve: Simplifying -3711015 + 70686x + 500x2 = 0 Solving -3711015 + 70686x + 500x2 = 0 Begin completing the square. Divide all terms by 500 the coefficient of the squared term: Divide each side by '500'. -7422.03 + 141.372x + x2 = 0.00 Move the constant term to the right: Add '7422.03' to each side of the equation. -7422.03 + 141.372x + 7422.03 + x2 = 0.00 + 7422.03 Reorder the terms: -7422.03 + 7422.03 + 141.372x + x2 = 0.00 + 7422.03 Combine like terms: -7422.03 + 7422.03 = 0.00 0.00 + 141.372x + x2 = 0.00 + 7422.03 141.372x + x2 = 0.00 + 7422.03 Combine like terms: 0.00 + 7422.03 = 7422.03 141.372x + x2 = 7422.03 The x term is 141.372x. Take half its coefficient (70.686). Square it (4996.510596) and add it to both sides. Add '4996.510596' to each side of the equation. 141.372x + 4996.510596 + x2 = 7422.03 + 4996.510596 Reorder the terms: 4996.510596 + 141.372x + x2 = 7422.03 + 4996.510596 Combine like terms: 7422.03 + 4996.510596 = 12418.540596 4996.510596 + 141.372x + x2 = 12418.540596 Factor a perfect square on the left side: (x + 70.686)(x + 70.686) = 12418.540596 Calculate the square root of the right side: 111.438505895 Break this problem into two subproblems by setting (x + 70.686) equal to 111.438505895 and -111.438505895.

Subproblem 1

x + 70.686 = 111.438505895 Simplifying x + 70.686 = 111.438505895 Reorder the terms: 70.686 + x = 111.438505895 Solving 70.686 + x = 111.438505895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-70.686' to each side of the equation. 70.686 + -70.686 + x = 111.438505895 + -70.686 Combine like terms: 70.686 + -70.686 = 0.000 0.000 + x = 111.438505895 + -70.686 x = 111.438505895 + -70.686 Combine like terms: 111.438505895 + -70.686 = 40.752505895 x = 40.752505895 Simplifying x = 40.752505895

Subproblem 2

x + 70.686 = -111.438505895 Simplifying x + 70.686 = -111.438505895 Reorder the terms: 70.686 + x = -111.438505895 Solving 70.686 + x = -111.438505895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-70.686' to each side of the equation. 70.686 + -70.686 + x = -111.438505895 + -70.686 Combine like terms: 70.686 + -70.686 = 0.000 0.000 + x = -111.438505895 + -70.686 x = -111.438505895 + -70.686 Combine like terms: -111.438505895 + -70.686 = -182.124505895 x = -182.124505895 Simplifying x = -182.124505895

Solution

The solution to the problem is based on the solutions from the subproblems. x = {40.752505895, -182.124505895}

Solution

x = {40.752505895, -182.124505895}

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