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Simplifying 0 = 0.00868x2 + -0.868x + 15.451 Reorder the terms: 0 = 15.451 + -0.868x + 0.00868x2 Solving 0 = 15.451 + -0.868x + 0.00868x2 Solving for variable 'x'. Combine like terms: 0 + -15.451 = -15.451 -15.451 + 0.868x + -0.00868x2 = 15.451 + -0.868x + 0.00868x2 + -15.451 + 0.868x + -0.00868x2 Reorder the terms: -15.451 + 0.868x + -0.00868x2 = 15.451 + -15.451 + -0.868x + 0.868x + 0.00868x2 + -0.00868x2 Combine like terms: 15.451 + -15.451 = 0.000 -15.451 + 0.868x + -0.00868x2 = 0.000 + -0.868x + 0.868x + 0.00868x2 + -0.00868x2 -15.451 + 0.868x + -0.00868x2 = -0.868x + 0.868x + 0.00868x2 + -0.00868x2 Combine like terms: -0.868x + 0.868x = 0.000 -15.451 + 0.868x + -0.00868x2 = 0.000 + 0.00868x2 + -0.00868x2 -15.451 + 0.868x + -0.00868x2 = 0.00868x2 + -0.00868x2 Combine like terms: 0.00868x2 + -0.00868x2 = 0.00000 -15.451 + 0.868x + -0.00868x2 = 0.00000 Begin completing the square. Divide all terms by -0.00868 the coefficient of the squared term: Divide each side by '-0.00868'. 1780.069124 + -100x + x2 = 0 Move the constant term to the right: Add '-1780.069124' to each side of the equation. 1780.069124 + -100x + -1780.069124 + x2 = 0 + -1780.069124 Reorder the terms: 1780.069124 + -1780.069124 + -100x + x2 = 0 + -1780.069124 Combine like terms: 1780.069124 + -1780.069124 = 0.000000 0.000000 + -100x + x2 = 0 + -1780.069124 -100x + x2 = 0 + -1780.069124 Combine like terms: 0 + -1780.069124 = -1780.069124 -100x + x2 = -1780.069124 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -1780.069124 + 2500 Reorder the terms: 2500 + -100x + x2 = -1780.069124 + 2500 Combine like terms: -1780.069124 + 2500 = 719.930876 2500 + -100x + x2 = 719.930876 Factor a perfect square on the left side: (x + -50)(x + -50) = 719.930876 Calculate the square root of the right side: 26.831527649 Break this problem into two subproblems by setting (x + -50) equal to 26.831527649 and -26.831527649.Subproblem 1
x + -50 = 26.831527649 Simplifying x + -50 = 26.831527649 Reorder the terms: -50 + x = 26.831527649 Solving -50 + x = 26.831527649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 26.831527649 + 50 Combine like terms: -50 + 50 = 0 0 + x = 26.831527649 + 50 x = 26.831527649 + 50 Combine like terms: 26.831527649 + 50 = 76.831527649 x = 76.831527649 Simplifying x = 76.831527649Subproblem 2
x + -50 = -26.831527649 Simplifying x + -50 = -26.831527649 Reorder the terms: -50 + x = -26.831527649 Solving -50 + x = -26.831527649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -26.831527649 + 50 Combine like terms: -50 + 50 = 0 0 + x = -26.831527649 + 50 x = -26.831527649 + 50 Combine like terms: -26.831527649 + 50 = 23.168472351 x = 23.168472351 Simplifying x = 23.168472351Solution
The solution to the problem is based on the solutions from the subproblems. x = {76.831527649, 23.168472351}
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