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Simplifying 370x + -2100 = x2 Reorder the terms: -2100 + 370x = x2 Solving -2100 + 370x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -2100 + 370x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2100 + -370x + x2 = 0 Move the constant term to the right: Add '-2100' to each side of the equation. 2100 + -370x + -2100 + x2 = 0 + -2100 Reorder the terms: 2100 + -2100 + -370x + x2 = 0 + -2100 Combine like terms: 2100 + -2100 = 0 0 + -370x + x2 = 0 + -2100 -370x + x2 = 0 + -2100 Combine like terms: 0 + -2100 = -2100 -370x + x2 = -2100 The x term is -370x. Take half its coefficient (-185). Square it (34225) and add it to both sides. Add '34225' to each side of the equation. -370x + 34225 + x2 = -2100 + 34225 Reorder the terms: 34225 + -370x + x2 = -2100 + 34225 Combine like terms: -2100 + 34225 = 32125 34225 + -370x + x2 = 32125 Factor a perfect square on the left side: (x + -185)(x + -185) = 32125 Calculate the square root of the right side: 179.234483289 Break this problem into two subproblems by setting (x + -185) equal to 179.234483289 and -179.234483289.Subproblem 1
x + -185 = 179.234483289 Simplifying x + -185 = 179.234483289 Reorder the terms: -185 + x = 179.234483289 Solving -185 + x = 179.234483289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '185' to each side of the equation. -185 + 185 + x = 179.234483289 + 185 Combine like terms: -185 + 185 = 0 0 + x = 179.234483289 + 185 x = 179.234483289 + 185 Combine like terms: 179.234483289 + 185 = 364.234483289 x = 364.234483289 Simplifying x = 364.234483289Subproblem 2
x + -185 = -179.234483289 Simplifying x + -185 = -179.234483289 Reorder the terms: -185 + x = -179.234483289 Solving -185 + x = -179.234483289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '185' to each side of the equation. -185 + 185 + x = -179.234483289 + 185 Combine like terms: -185 + 185 = 0 0 + x = -179.234483289 + 185 x = -179.234483289 + 185 Combine like terms: -179.234483289 + 185 = 5.765516711 x = 5.765516711 Simplifying x = 5.765516711Solution
The solution to the problem is based on the solutions from the subproblems. x = {364.234483289, 5.765516711}
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