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Simplifying 0 = -0.02x2 + x + 6 Reorder the terms: 0 = 6 + x + -0.02x2 Solving 0 = 6 + x + -0.02x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -1x + 0.02x2 = 6 + x + -0.02x2 + -6 + -1x + 0.02x2 Reorder the terms: -6 + -1x + 0.02x2 = 6 + -6 + x + -1x + -0.02x2 + 0.02x2 Combine like terms: 6 + -6 = 0 -6 + -1x + 0.02x2 = 0 + x + -1x + -0.02x2 + 0.02x2 -6 + -1x + 0.02x2 = x + -1x + -0.02x2 + 0.02x2 Combine like terms: x + -1x = 0 -6 + -1x + 0.02x2 = 0 + -0.02x2 + 0.02x2 -6 + -1x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 -6 + -1x + 0.02x2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -300 + -50x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + -50x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -50x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -50x + x2 = 0 + 300 -50x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -50x + x2 = 300 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 300 + 625 Reorder the terms: 625 + -50x + x2 = 300 + 625 Combine like terms: 300 + 625 = 925 625 + -50x + x2 = 925 Factor a perfect square on the left side: (x + -25)(x + -25) = 925 Calculate the square root of the right side: 30.413812651 Break this problem into two subproblems by setting (x + -25) equal to 30.413812651 and -30.413812651.Subproblem 1
x + -25 = 30.413812651 Simplifying x + -25 = 30.413812651 Reorder the terms: -25 + x = 30.413812651 Solving -25 + x = 30.413812651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 30.413812651 + 25 Combine like terms: -25 + 25 = 0 0 + x = 30.413812651 + 25 x = 30.413812651 + 25 Combine like terms: 30.413812651 + 25 = 55.413812651 x = 55.413812651 Simplifying x = 55.413812651Subproblem 2
x + -25 = -30.413812651 Simplifying x + -25 = -30.413812651 Reorder the terms: -25 + x = -30.413812651 Solving -25 + x = -30.413812651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -30.413812651 + 25 Combine like terms: -25 + 25 = 0 0 + x = -30.413812651 + 25 x = -30.413812651 + 25 Combine like terms: -30.413812651 + 25 = -5.413812651 x = -5.413812651 Simplifying x = -5.413812651Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.413812651, -5.413812651}
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