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Simplifying 0 = 0.45x2 + 7x + -9075 Reorder the terms: 0 = -9075 + 7x + 0.45x2 Solving 0 = -9075 + 7x + 0.45x2 Solving for variable 'x'. Combine like terms: 0 + 9075 = 9075 9075 + -7x + -0.45x2 = -9075 + 7x + 0.45x2 + 9075 + -7x + -0.45x2 Reorder the terms: 9075 + -7x + -0.45x2 = -9075 + 9075 + 7x + -7x + 0.45x2 + -0.45x2 Combine like terms: -9075 + 9075 = 0 9075 + -7x + -0.45x2 = 0 + 7x + -7x + 0.45x2 + -0.45x2 9075 + -7x + -0.45x2 = 7x + -7x + 0.45x2 + -0.45x2 Combine like terms: 7x + -7x = 0 9075 + -7x + -0.45x2 = 0 + 0.45x2 + -0.45x2 9075 + -7x + -0.45x2 = 0.45x2 + -0.45x2 Combine like terms: 0.45x2 + -0.45x2 = 0.00 9075 + -7x + -0.45x2 = 0.00 Begin completing the square. Divide all terms by -0.45 the coefficient of the squared term: Divide each side by '-0.45'. -20166.66667 + 15.55555556x + x2 = 0 Move the constant term to the right: Add '20166.66667' to each side of the equation. -20166.66667 + 15.55555556x + 20166.66667 + x2 = 0 + 20166.66667 Reorder the terms: -20166.66667 + 20166.66667 + 15.55555556x + x2 = 0 + 20166.66667 Combine like terms: -20166.66667 + 20166.66667 = 0.00000 0.00000 + 15.55555556x + x2 = 0 + 20166.66667 15.55555556x + x2 = 0 + 20166.66667 Combine like terms: 0 + 20166.66667 = 20166.66667 15.55555556x + x2 = 20166.66667 The x term is 15.55555556x. Take half its coefficient (7.77777778). Square it (60.49382720) and add it to both sides. Add '60.49382720' to each side of the equation. 15.55555556x + 60.49382720 + x2 = 20166.66667 + 60.49382720 Reorder the terms: 60.49382720 + 15.55555556x + x2 = 20166.66667 + 60.49382720 Combine like terms: 20166.66667 + 60.49382720 = 20227.1604972 60.49382720 + 15.55555556x + x2 = 20227.1604972 Factor a perfect square on the left side: (x + 7.77777778)(x + 7.77777778) = 20227.1604972 Calculate the square root of the right side: 142.222222234 Break this problem into two subproblems by setting (x + 7.77777778) equal to 142.222222234 and -142.222222234.Subproblem 1
x + 7.77777778 = 142.222222234 Simplifying x + 7.77777778 = 142.222222234 Reorder the terms: 7.77777778 + x = 142.222222234 Solving 7.77777778 + x = 142.222222234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.77777778' to each side of the equation. 7.77777778 + -7.77777778 + x = 142.222222234 + -7.77777778 Combine like terms: 7.77777778 + -7.77777778 = 0.00000000 0.00000000 + x = 142.222222234 + -7.77777778 x = 142.222222234 + -7.77777778 Combine like terms: 142.222222234 + -7.77777778 = 134.444444454 x = 134.444444454 Simplifying x = 134.444444454Subproblem 2
x + 7.77777778 = -142.222222234 Simplifying x + 7.77777778 = -142.222222234 Reorder the terms: 7.77777778 + x = -142.222222234 Solving 7.77777778 + x = -142.222222234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.77777778' to each side of the equation. 7.77777778 + -7.77777778 + x = -142.222222234 + -7.77777778 Combine like terms: 7.77777778 + -7.77777778 = 0.00000000 0.00000000 + x = -142.222222234 + -7.77777778 x = -142.222222234 + -7.77777778 Combine like terms: -142.222222234 + -7.77777778 = -150.000000014 x = -150.000000014 Simplifying x = -150.000000014Solution
The solution to the problem is based on the solutions from the subproblems. x = {134.444444454, -150.000000014}
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