700000=-2x^2+4000x

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Solution for 700000=-2x^2+4000x equation:


Simplifying
700000 = -2x2 + 4000x

Reorder the terms:
700000 = 4000x + -2x2

Solving
700000 = 4000x + -2x2

Solving for variable 'x'.

Reorder the terms:
700000 + -4000x + 2x2 = 4000x + -4000x + -2x2 + 2x2

Combine like terms: 4000x + -4000x = 0
700000 + -4000x + 2x2 = 0 + -2x2 + 2x2
700000 + -4000x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
700000 + -4000x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(350000 + -2000x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(350000 + -2000x + x2)' equal to zero and attempt to solve: Simplifying 350000 + -2000x + x2 = 0 Solving 350000 + -2000x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-350000' to each side of the equation. 350000 + -2000x + -350000 + x2 = 0 + -350000 Reorder the terms: 350000 + -350000 + -2000x + x2 = 0 + -350000 Combine like terms: 350000 + -350000 = 0 0 + -2000x + x2 = 0 + -350000 -2000x + x2 = 0 + -350000 Combine like terms: 0 + -350000 = -350000 -2000x + x2 = -350000 The x term is -2000x. Take half its coefficient (-1000). Square it (1000000) and add it to both sides. Add '1000000' to each side of the equation. -2000x + 1000000 + x2 = -350000 + 1000000 Reorder the terms: 1000000 + -2000x + x2 = -350000 + 1000000 Combine like terms: -350000 + 1000000 = 650000 1000000 + -2000x + x2 = 650000 Factor a perfect square on the left side: (x + -1000)(x + -1000) = 650000 Calculate the square root of the right side: 806.22577483 Break this problem into two subproblems by setting (x + -1000) equal to 806.22577483 and -806.22577483.

Subproblem 1

x + -1000 = 806.22577483 Simplifying x + -1000 = 806.22577483 Reorder the terms: -1000 + x = 806.22577483 Solving -1000 + x = 806.22577483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = 806.22577483 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = 806.22577483 + 1000 x = 806.22577483 + 1000 Combine like terms: 806.22577483 + 1000 = 1806.22577483 x = 1806.22577483 Simplifying x = 1806.22577483

Subproblem 2

x + -1000 = -806.22577483 Simplifying x + -1000 = -806.22577483 Reorder the terms: -1000 + x = -806.22577483 Solving -1000 + x = -806.22577483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = -806.22577483 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = -806.22577483 + 1000 x = -806.22577483 + 1000 Combine like terms: -806.22577483 + 1000 = 193.77422517 x = 193.77422517 Simplifying x = 193.77422517

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1806.22577483, 193.77422517}

Solution

x = {1806.22577483, 193.77422517}

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