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Simplifying -1x2 + 800x + -2300 = 110000 Reorder the terms: -2300 + 800x + -1x2 = 110000 Solving -2300 + 800x + -1x2 = 110000 Solving for variable 'x'. Reorder the terms: -2300 + -110000 + 800x + -1x2 = 110000 + -110000 Combine like terms: -2300 + -110000 = -112300 -112300 + 800x + -1x2 = 110000 + -110000 Combine like terms: 110000 + -110000 = 0 -112300 + 800x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 112300 + -800x + x2 = 0 Move the constant term to the right: Add '-112300' to each side of the equation. 112300 + -800x + -112300 + x2 = 0 + -112300 Reorder the terms: 112300 + -112300 + -800x + x2 = 0 + -112300 Combine like terms: 112300 + -112300 = 0 0 + -800x + x2 = 0 + -112300 -800x + x2 = 0 + -112300 Combine like terms: 0 + -112300 = -112300 -800x + x2 = -112300 The x term is -800x. Take half its coefficient (-400). Square it (160000) and add it to both sides. Add '160000' to each side of the equation. -800x + 160000 + x2 = -112300 + 160000 Reorder the terms: 160000 + -800x + x2 = -112300 + 160000 Combine like terms: -112300 + 160000 = 47700 160000 + -800x + x2 = 47700 Factor a perfect square on the left side: (x + -400)(x + -400) = 47700 Calculate the square root of the right side: 218.403296678 Break this problem into two subproblems by setting (x + -400) equal to 218.403296678 and -218.403296678.Subproblem 1
x + -400 = 218.403296678 Simplifying x + -400 = 218.403296678 Reorder the terms: -400 + x = 218.403296678 Solving -400 + x = 218.403296678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = 218.403296678 + 400 Combine like terms: -400 + 400 = 0 0 + x = 218.403296678 + 400 x = 218.403296678 + 400 Combine like terms: 218.403296678 + 400 = 618.403296678 x = 618.403296678 Simplifying x = 618.403296678Subproblem 2
x + -400 = -218.403296678 Simplifying x + -400 = -218.403296678 Reorder the terms: -400 + x = -218.403296678 Solving -400 + x = -218.403296678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = -218.403296678 + 400 Combine like terms: -400 + 400 = 0 0 + x = -218.403296678 + 400 x = -218.403296678 + 400 Combine like terms: -218.403296678 + 400 = 181.596703322 x = 181.596703322 Simplifying x = 181.596703322Solution
The solution to the problem is based on the solutions from the subproblems. x = {618.403296678, 181.596703322}
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