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Simplifying 10 = 0.002x2 + 0.005x + -0.029 Reorder the terms: 10 = -0.029 + 0.005x + 0.002x2 Solving 10 = -0.029 + 0.005x + 0.002x2 Solving for variable 'x'. Combine like terms: 10 + 0.029 = 10.029 10.029 + -0.005x + -0.002x2 = -0.029 + 0.005x + 0.002x2 + 0.029 + -0.005x + -0.002x2 Reorder the terms: 10.029 + -0.005x + -0.002x2 = -0.029 + 0.029 + 0.005x + -0.005x + 0.002x2 + -0.002x2 Combine like terms: -0.029 + 0.029 = 0.000 10.029 + -0.005x + -0.002x2 = 0.000 + 0.005x + -0.005x + 0.002x2 + -0.002x2 10.029 + -0.005x + -0.002x2 = 0.005x + -0.005x + 0.002x2 + -0.002x2 Combine like terms: 0.005x + -0.005x = 0.000 10.029 + -0.005x + -0.002x2 = 0.000 + 0.002x2 + -0.002x2 10.029 + -0.005x + -0.002x2 = 0.002x2 + -0.002x2 Combine like terms: 0.002x2 + -0.002x2 = 0.000 10.029 + -0.005x + -0.002x2 = 0.000 Begin completing the square. Divide all terms by -0.002 the coefficient of the squared term: Divide each side by '-0.002'. -5014.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '5014.5' to each side of the equation. -5014.5 + 2.5x + 5014.5 + x2 = 0 + 5014.5 Reorder the terms: -5014.5 + 5014.5 + 2.5x + x2 = 0 + 5014.5 Combine like terms: -5014.5 + 5014.5 = 0.0 0.0 + 2.5x + x2 = 0 + 5014.5 2.5x + x2 = 0 + 5014.5 Combine like terms: 0 + 5014.5 = 5014.5 2.5x + x2 = 5014.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 5014.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 5014.5 + 1.5625 Combine like terms: 5014.5 + 1.5625 = 5016.0625 1.5625 + 2.5x + x2 = 5016.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 5016.0625 Calculate the square root of the right side: 70.824166073 Break this problem into two subproblems by setting (x + 1.25) equal to 70.824166073 and -70.824166073.Subproblem 1
x + 1.25 = 70.824166073 Simplifying x + 1.25 = 70.824166073 Reorder the terms: 1.25 + x = 70.824166073 Solving 1.25 + x = 70.824166073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 70.824166073 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 70.824166073 + -1.25 x = 70.824166073 + -1.25 Combine like terms: 70.824166073 + -1.25 = 69.574166073 x = 69.574166073 Simplifying x = 69.574166073Subproblem 2
x + 1.25 = -70.824166073 Simplifying x + 1.25 = -70.824166073 Reorder the terms: 1.25 + x = -70.824166073 Solving 1.25 + x = -70.824166073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -70.824166073 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -70.824166073 + -1.25 x = -70.824166073 + -1.25 Combine like terms: -70.824166073 + -1.25 = -72.074166073 x = -72.074166073 Simplifying x = -72.074166073Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.574166073, -72.074166073}
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