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Simplifying x(x + 107.8) = 197.3 Reorder the terms: x(107.8 + x) = 197.3 (107.8 * x + x * x) = 197.3 (107.8x + x2) = 197.3 Solving 107.8x + x2 = 197.3 Solving for variable 'x'. Reorder the terms: -197.3 + 107.8x + x2 = 197.3 + -197.3 Combine like terms: 197.3 + -197.3 = 0.0 -197.3 + 107.8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '197.3' to each side of the equation. -197.3 + 107.8x + 197.3 + x2 = 0.0 + 197.3 Reorder the terms: -197.3 + 197.3 + 107.8x + x2 = 0.0 + 197.3 Combine like terms: -197.3 + 197.3 = 0.0 0.0 + 107.8x + x2 = 0.0 + 197.3 107.8x + x2 = 0.0 + 197.3 Combine like terms: 0.0 + 197.3 = 197.3 107.8x + x2 = 197.3 The x term is 107.8x. Take half its coefficient (53.9). Square it (2905.21) and add it to both sides. Add '2905.21' to each side of the equation. 107.8x + 2905.21 + x2 = 197.3 + 2905.21 Reorder the terms: 2905.21 + 107.8x + x2 = 197.3 + 2905.21 Combine like terms: 197.3 + 2905.21 = 3102.51 2905.21 + 107.8x + x2 = 3102.51 Factor a perfect square on the left side: (x + 53.9)(x + 53.9) = 3102.51 Calculate the square root of the right side: 55.700179533 Break this problem into two subproblems by setting (x + 53.9) equal to 55.700179533 and -55.700179533.Subproblem 1
x + 53.9 = 55.700179533 Simplifying x + 53.9 = 55.700179533 Reorder the terms: 53.9 + x = 55.700179533 Solving 53.9 + x = 55.700179533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-53.9' to each side of the equation. 53.9 + -53.9 + x = 55.700179533 + -53.9 Combine like terms: 53.9 + -53.9 = 0.0 0.0 + x = 55.700179533 + -53.9 x = 55.700179533 + -53.9 Combine like terms: 55.700179533 + -53.9 = 1.800179533 x = 1.800179533 Simplifying x = 1.800179533Subproblem 2
x + 53.9 = -55.700179533 Simplifying x + 53.9 = -55.700179533 Reorder the terms: 53.9 + x = -55.700179533 Solving 53.9 + x = -55.700179533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-53.9' to each side of the equation. 53.9 + -53.9 + x = -55.700179533 + -53.9 Combine like terms: 53.9 + -53.9 = 0.0 0.0 + x = -55.700179533 + -53.9 x = -55.700179533 + -53.9 Combine like terms: -55.700179533 + -53.9 = -109.600179533 x = -109.600179533 Simplifying x = -109.600179533Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.800179533, -109.600179533}
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