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Simplifying 830x + -1x2 + -1(2300 + 70x) = 0 830x + -1x2 + (2300 * -1 + 70x * -1) = 0 830x + -1x2 + (-2300 + -70x) = 0 Reorder the terms: -2300 + 830x + -70x + -1x2 = 0 Combine like terms: 830x + -70x = 760x -2300 + 760x + -1x2 = 0 Solving -2300 + 760x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2300 + -760x + x2 = 0 Move the constant term to the right: Add '-2300' to each side of the equation. 2300 + -760x + -2300 + x2 = 0 + -2300 Reorder the terms: 2300 + -2300 + -760x + x2 = 0 + -2300 Combine like terms: 2300 + -2300 = 0 0 + -760x + x2 = 0 + -2300 -760x + x2 = 0 + -2300 Combine like terms: 0 + -2300 = -2300 -760x + x2 = -2300 The x term is -760x. Take half its coefficient (-380). Square it (144400) and add it to both sides. Add '144400' to each side of the equation. -760x + 144400 + x2 = -2300 + 144400 Reorder the terms: 144400 + -760x + x2 = -2300 + 144400 Combine like terms: -2300 + 144400 = 142100 144400 + -760x + x2 = 142100 Factor a perfect square on the left side: (x + -380)(x + -380) = 142100 Calculate the square root of the right side: 376.961536499 Break this problem into two subproblems by setting (x + -380) equal to 376.961536499 and -376.961536499.Subproblem 1
x + -380 = 376.961536499 Simplifying x + -380 = 376.961536499 Reorder the terms: -380 + x = 376.961536499 Solving -380 + x = 376.961536499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '380' to each side of the equation. -380 + 380 + x = 376.961536499 + 380 Combine like terms: -380 + 380 = 0 0 + x = 376.961536499 + 380 x = 376.961536499 + 380 Combine like terms: 376.961536499 + 380 = 756.961536499 x = 756.961536499 Simplifying x = 756.961536499Subproblem 2
x + -380 = -376.961536499 Simplifying x + -380 = -376.961536499 Reorder the terms: -380 + x = -376.961536499 Solving -380 + x = -376.961536499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '380' to each side of the equation. -380 + 380 + x = -376.961536499 + 380 Combine like terms: -380 + 380 = 0 0 + x = -376.961536499 + 380 x = -376.961536499 + 380 Combine like terms: -376.961536499 + 380 = 3.038463501 x = 3.038463501 Simplifying x = 3.038463501Solution
The solution to the problem is based on the solutions from the subproblems. x = {756.961536499, 3.038463501}
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