x^2+1750x+765625=1465625

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Solution for x^2+1750x+765625=1465625 equation:


Simplifying
x2 + 1750x + 765625 = 1465625

Reorder the terms:
765625 + 1750x + x2 = 1465625

Solving
765625 + 1750x + x2 = 1465625

Solving for variable 'x'.

Reorder the terms:
765625 + -1465625 + 1750x + x2 = 1465625 + -1465625

Combine like terms: 765625 + -1465625 = -700000
-700000 + 1750x + x2 = 1465625 + -1465625

Combine like terms: 1465625 + -1465625 = 0
-700000 + 1750x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '700000' to each side of the equation.
-700000 + 1750x + 700000 + x2 = 0 + 700000

Reorder the terms:
-700000 + 700000 + 1750x + x2 = 0 + 700000

Combine like terms: -700000 + 700000 = 0
0 + 1750x + x2 = 0 + 700000
1750x + x2 = 0 + 700000

Combine like terms: 0 + 700000 = 700000
1750x + x2 = 700000

The x term is 1750x.  Take half its coefficient (875).
Square it (765625) and add it to both sides.

Add '765625' to each side of the equation.
1750x + 765625 + x2 = 700000 + 765625

Reorder the terms:
765625 + 1750x + x2 = 700000 + 765625

Combine like terms: 700000 + 765625 = 1465625
765625 + 1750x + x2 = 1465625

Factor a perfect square on the left side:
(x + 875)(x + 875) = 1465625

Calculate the square root of the right side: 1210.63000128

Break this problem into two subproblems by setting 
(x + 875) equal to 1210.63000128 and -1210.63000128.

Subproblem 1

x + 875 = 1210.63000128 Simplifying x + 875 = 1210.63000128 Reorder the terms: 875 + x = 1210.63000128 Solving 875 + x = 1210.63000128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-875' to each side of the equation. 875 + -875 + x = 1210.63000128 + -875 Combine like terms: 875 + -875 = 0 0 + x = 1210.63000128 + -875 x = 1210.63000128 + -875 Combine like terms: 1210.63000128 + -875 = 335.63000128 x = 335.63000128 Simplifying x = 335.63000128

Subproblem 2

x + 875 = -1210.63000128 Simplifying x + 875 = -1210.63000128 Reorder the terms: 875 + x = -1210.63000128 Solving 875 + x = -1210.63000128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-875' to each side of the equation. 875 + -875 + x = -1210.63000128 + -875 Combine like terms: 875 + -875 = 0 0 + x = -1210.63000128 + -875 x = -1210.63000128 + -875 Combine like terms: -1210.63000128 + -875 = -2085.63000128 x = -2085.63000128 Simplifying x = -2085.63000128

Solution

The solution to the problem is based on the solutions from the subproblems. x = {335.63000128, -2085.63000128}

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