15000=26x^2+168x+4208

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Solution for 15000=26x^2+168x+4208 equation:


Simplifying
15000 = 26x2 + 168x + 4208

Reorder the terms:
15000 = 4208 + 168x + 26x2

Solving
15000 = 4208 + 168x + 26x2

Solving for variable 'x'.

Combine like terms: 15000 + -4208 = 10792
10792 + -168x + -26x2 = 4208 + 168x + 26x2 + -4208 + -168x + -26x2

Reorder the terms:
10792 + -168x + -26x2 = 4208 + -4208 + 168x + -168x + 26x2 + -26x2

Combine like terms: 4208 + -4208 = 0
10792 + -168x + -26x2 = 0 + 168x + -168x + 26x2 + -26x2
10792 + -168x + -26x2 = 168x + -168x + 26x2 + -26x2

Combine like terms: 168x + -168x = 0
10792 + -168x + -26x2 = 0 + 26x2 + -26x2
10792 + -168x + -26x2 = 26x2 + -26x2

Combine like terms: 26x2 + -26x2 = 0
10792 + -168x + -26x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5396 + -84x + -13x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5396 + -84x + -13x2)' equal to zero and attempt to solve: Simplifying 5396 + -84x + -13x2 = 0 Solving 5396 + -84x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -415.0769231 + 6.461538462x + x2 = 0 Move the constant term to the right: Add '415.0769231' to each side of the equation. -415.0769231 + 6.461538462x + 415.0769231 + x2 = 0 + 415.0769231 Reorder the terms: -415.0769231 + 415.0769231 + 6.461538462x + x2 = 0 + 415.0769231 Combine like terms: -415.0769231 + 415.0769231 = 0.0000000 0.0000000 + 6.461538462x + x2 = 0 + 415.0769231 6.461538462x + x2 = 0 + 415.0769231 Combine like terms: 0 + 415.0769231 = 415.0769231 6.461538462x + x2 = 415.0769231 The x term is 6.461538462x. Take half its coefficient (3.230769231). Square it (10.43786982) and add it to both sides. Add '10.43786982' to each side of the equation. 6.461538462x + 10.43786982 + x2 = 415.0769231 + 10.43786982 Reorder the terms: 10.43786982 + 6.461538462x + x2 = 415.0769231 + 10.43786982 Combine like terms: 415.0769231 + 10.43786982 = 425.51479292 10.43786982 + 6.461538462x + x2 = 425.51479292 Factor a perfect square on the left side: (x + 3.230769231)(x + 3.230769231) = 425.51479292 Calculate the square root of the right side: 20.628009912 Break this problem into two subproblems by setting (x + 3.230769231) equal to 20.628009912 and -20.628009912.

Subproblem 1

x + 3.230769231 = 20.628009912 Simplifying x + 3.230769231 = 20.628009912 Reorder the terms: 3.230769231 + x = 20.628009912 Solving 3.230769231 + x = 20.628009912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.230769231' to each side of the equation. 3.230769231 + -3.230769231 + x = 20.628009912 + -3.230769231 Combine like terms: 3.230769231 + -3.230769231 = 0.000000000 0.000000000 + x = 20.628009912 + -3.230769231 x = 20.628009912 + -3.230769231 Combine like terms: 20.628009912 + -3.230769231 = 17.397240681 x = 17.397240681 Simplifying x = 17.397240681

Subproblem 2

x + 3.230769231 = -20.628009912 Simplifying x + 3.230769231 = -20.628009912 Reorder the terms: 3.230769231 + x = -20.628009912 Solving 3.230769231 + x = -20.628009912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.230769231' to each side of the equation. 3.230769231 + -3.230769231 + x = -20.628009912 + -3.230769231 Combine like terms: 3.230769231 + -3.230769231 = 0.000000000 0.000000000 + x = -20.628009912 + -3.230769231 x = -20.628009912 + -3.230769231 Combine like terms: -20.628009912 + -3.230769231 = -23.858779143 x = -23.858779143 Simplifying x = -23.858779143

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.397240681, -23.858779143}

Solution

x = {17.397240681, -23.858779143}

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