3125=x^2+630x+65000

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Solution for 3125=x^2+630x+65000 equation:


Simplifying
3125 = x2 + 630x + 65000

Reorder the terms:
3125 = 65000 + 630x + x2

Solving
3125 = 65000 + 630x + x2

Solving for variable 'x'.

Combine like terms: 3125 + -65000 = -61875
-61875 + -630x + -1x2 = 65000 + 630x + x2 + -65000 + -630x + -1x2

Reorder the terms:
-61875 + -630x + -1x2 = 65000 + -65000 + 630x + -630x + x2 + -1x2

Combine like terms: 65000 + -65000 = 0
-61875 + -630x + -1x2 = 0 + 630x + -630x + x2 + -1x2
-61875 + -630x + -1x2 = 630x + -630x + x2 + -1x2

Combine like terms: 630x + -630x = 0
-61875 + -630x + -1x2 = 0 + x2 + -1x2
-61875 + -630x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-61875 + -630x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(61875 + 630x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(61875 + 630x + x2)' equal to zero and attempt to solve: Simplifying 61875 + 630x + x2 = 0 Solving 61875 + 630x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-61875' to each side of the equation. 61875 + 630x + -61875 + x2 = 0 + -61875 Reorder the terms: 61875 + -61875 + 630x + x2 = 0 + -61875 Combine like terms: 61875 + -61875 = 0 0 + 630x + x2 = 0 + -61875 630x + x2 = 0 + -61875 Combine like terms: 0 + -61875 = -61875 630x + x2 = -61875 The x term is 630x. Take half its coefficient (315). Square it (99225) and add it to both sides. Add '99225' to each side of the equation. 630x + 99225 + x2 = -61875 + 99225 Reorder the terms: 99225 + 630x + x2 = -61875 + 99225 Combine like terms: -61875 + 99225 = 37350 99225 + 630x + x2 = 37350 Factor a perfect square on the left side: (x + 315)(x + 315) = 37350 Calculate the square root of the right side: 193.261480901 Break this problem into two subproblems by setting (x + 315) equal to 193.261480901 and -193.261480901.

Subproblem 1

x + 315 = 193.261480901 Simplifying x + 315 = 193.261480901 Reorder the terms: 315 + x = 193.261480901 Solving 315 + x = 193.261480901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-315' to each side of the equation. 315 + -315 + x = 193.261480901 + -315 Combine like terms: 315 + -315 = 0 0 + x = 193.261480901 + -315 x = 193.261480901 + -315 Combine like terms: 193.261480901 + -315 = -121.738519099 x = -121.738519099 Simplifying x = -121.738519099

Subproblem 2

x + 315 = -193.261480901 Simplifying x + 315 = -193.261480901 Reorder the terms: 315 + x = -193.261480901 Solving 315 + x = -193.261480901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-315' to each side of the equation. 315 + -315 + x = -193.261480901 + -315 Combine like terms: 315 + -315 = 0 0 + x = -193.261480901 + -315 x = -193.261480901 + -315 Combine like terms: -193.261480901 + -315 = -508.261480901 x = -508.261480901 Simplifying x = -508.261480901

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-121.738519099, -508.261480901}

Solution

x = {-121.738519099, -508.261480901}

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