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Simplifying 17x2 + 8x + -2400 = 0 Reorder the terms: -2400 + 8x + 17x2 = 0 Solving -2400 + 8x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -141.1764706 + 0.4705882353x + x2 = 0 Move the constant term to the right: Add '141.1764706' to each side of the equation. -141.1764706 + 0.4705882353x + 141.1764706 + x2 = 0 + 141.1764706 Reorder the terms: -141.1764706 + 141.1764706 + 0.4705882353x + x2 = 0 + 141.1764706 Combine like terms: -141.1764706 + 141.1764706 = 0.0000000 0.0000000 + 0.4705882353x + x2 = 0 + 141.1764706 0.4705882353x + x2 = 0 + 141.1764706 Combine like terms: 0 + 141.1764706 = 141.1764706 0.4705882353x + x2 = 141.1764706 The x term is 0.4705882353x. Take half its coefficient (0.2352941177). Square it (0.05536332182) and add it to both sides. Add '0.05536332182' to each side of the equation. 0.4705882353x + 0.05536332182 + x2 = 141.1764706 + 0.05536332182 Reorder the terms: 0.05536332182 + 0.4705882353x + x2 = 141.1764706 + 0.05536332182 Combine like terms: 141.1764706 + 0.05536332182 = 141.23183392182 0.05536332182 + 0.4705882353x + x2 = 141.23183392182 Factor a perfect square on the left side: (x + 0.2352941177)(x + 0.2352941177) = 141.23183392182 Calculate the square root of the right side: 11.884100047 Break this problem into two subproblems by setting (x + 0.2352941177) equal to 11.884100047 and -11.884100047.Subproblem 1
x + 0.2352941177 = 11.884100047 Simplifying x + 0.2352941177 = 11.884100047 Reorder the terms: 0.2352941177 + x = 11.884100047 Solving 0.2352941177 + x = 11.884100047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2352941177' to each side of the equation. 0.2352941177 + -0.2352941177 + x = 11.884100047 + -0.2352941177 Combine like terms: 0.2352941177 + -0.2352941177 = 0.0000000000 0.0000000000 + x = 11.884100047 + -0.2352941177 x = 11.884100047 + -0.2352941177 Combine like terms: 11.884100047 + -0.2352941177 = 11.6488059293 x = 11.6488059293 Simplifying x = 11.6488059293Subproblem 2
x + 0.2352941177 = -11.884100047 Simplifying x + 0.2352941177 = -11.884100047 Reorder the terms: 0.2352941177 + x = -11.884100047 Solving 0.2352941177 + x = -11.884100047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2352941177' to each side of the equation. 0.2352941177 + -0.2352941177 + x = -11.884100047 + -0.2352941177 Combine like terms: 0.2352941177 + -0.2352941177 = 0.0000000000 0.0000000000 + x = -11.884100047 + -0.2352941177 x = -11.884100047 + -0.2352941177 Combine like terms: -11.884100047 + -0.2352941177 = -12.1193941647 x = -12.1193941647 Simplifying x = -12.1193941647Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.6488059293, -12.1193941647}
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