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Simplifying 0.01x2 + -154x + 525300 = 0 Reorder the terms: 525300 + -154x + 0.01x2 = 0 Solving 525300 + -154x + 0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 52530000 + -15400x + x2 = 0 Move the constant term to the right: Add '-52530000' to each side of the equation. 52530000 + -15400x + -52530000 + x2 = 0 + -52530000 Reorder the terms: 52530000 + -52530000 + -15400x + x2 = 0 + -52530000 Combine like terms: 52530000 + -52530000 = 0 0 + -15400x + x2 = 0 + -52530000 -15400x + x2 = 0 + -52530000 Combine like terms: 0 + -52530000 = -52530000 -15400x + x2 = -52530000 The x term is -15400x. Take half its coefficient (-7700). Square it (59290000) and add it to both sides. Add '59290000' to each side of the equation. -15400x + 59290000 + x2 = -52530000 + 59290000 Reorder the terms: 59290000 + -15400x + x2 = -52530000 + 59290000 Combine like terms: -52530000 + 59290000 = 6760000 59290000 + -15400x + x2 = 6760000 Factor a perfect square on the left side: (x + -7700)(x + -7700) = 6760000 Calculate the square root of the right side: 2600 Break this problem into two subproblems by setting (x + -7700) equal to 2600 and -2600.Subproblem 1
x + -7700 = 2600 Simplifying x + -7700 = 2600 Reorder the terms: -7700 + x = 2600 Solving -7700 + x = 2600 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7700' to each side of the equation. -7700 + 7700 + x = 2600 + 7700 Combine like terms: -7700 + 7700 = 0 0 + x = 2600 + 7700 x = 2600 + 7700 Combine like terms: 2600 + 7700 = 10300 x = 10300 Simplifying x = 10300Subproblem 2
x + -7700 = -2600 Simplifying x + -7700 = -2600 Reorder the terms: -7700 + x = -2600 Solving -7700 + x = -2600 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7700' to each side of the equation. -7700 + 7700 + x = -2600 + 7700 Combine like terms: -7700 + 7700 = 0 0 + x = -2600 + 7700 x = -2600 + 7700 Combine like terms: -2600 + 7700 = 5100 x = 5100 Simplifying x = 5100Solution
The solution to the problem is based on the solutions from the subproblems. x = {10300, 5100}
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