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Simplifying x2 + -35.6x + 300.84 = 0 Reorder the terms: 300.84 + -35.6x + x2 = 0 Solving 300.84 + -35.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-300.84' to each side of the equation. 300.84 + -35.6x + -300.84 + x2 = 0 + -300.84 Reorder the terms: 300.84 + -300.84 + -35.6x + x2 = 0 + -300.84 Combine like terms: 300.84 + -300.84 = 0.00 0.00 + -35.6x + x2 = 0 + -300.84 -35.6x + x2 = 0 + -300.84 Combine like terms: 0 + -300.84 = -300.84 -35.6x + x2 = -300.84 The x term is -35.6x. Take half its coefficient (-17.8). Square it (316.84) and add it to both sides. Add '316.84' to each side of the equation. -35.6x + 316.84 + x2 = -300.84 + 316.84 Reorder the terms: 316.84 + -35.6x + x2 = -300.84 + 316.84 Combine like terms: -300.84 + 316.84 = 16 316.84 + -35.6x + x2 = 16 Factor a perfect square on the left side: (x + -17.8)(x + -17.8) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + -17.8) equal to 4 and -4.Subproblem 1
x + -17.8 = 4 Simplifying x + -17.8 = 4 Reorder the terms: -17.8 + x = 4 Solving -17.8 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.8' to each side of the equation. -17.8 + 17.8 + x = 4 + 17.8 Combine like terms: -17.8 + 17.8 = 0.0 0.0 + x = 4 + 17.8 x = 4 + 17.8 Combine like terms: 4 + 17.8 = 21.8 x = 21.8 Simplifying x = 21.8Subproblem 2
x + -17.8 = -4 Simplifying x + -17.8 = -4 Reorder the terms: -17.8 + x = -4 Solving -17.8 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.8' to each side of the equation. -17.8 + 17.8 + x = -4 + 17.8 Combine like terms: -17.8 + 17.8 = 0.0 0.0 + x = -4 + 17.8 x = -4 + 17.8 Combine like terms: -4 + 17.8 = 13.8 x = 13.8 Simplifying x = 13.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.8, 13.8}
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