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Simplifying 9x2 + 23x + -28 = 0 Reorder the terms: -28 + 23x + 9x2 = 0 Solving -28 + 23x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.111111111 + 2.555555556x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + 2.555555556x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + 2.555555556x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + 2.555555556x + x2 = 0 + 3.111111111 2.555555556x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 2.555555556x + x2 = 3.111111111 The x term is 2.555555556x. Take half its coefficient (1.277777778). Square it (1.632716050) and add it to both sides. Add '1.632716050' to each side of the equation. 2.555555556x + 1.632716050 + x2 = 3.111111111 + 1.632716050 Reorder the terms: 1.632716050 + 2.555555556x + x2 = 3.111111111 + 1.632716050 Combine like terms: 3.111111111 + 1.632716050 = 4.743827161 1.632716050 + 2.555555556x + x2 = 4.743827161 Factor a perfect square on the left side: (x + 1.277777778)(x + 1.277777778) = 4.743827161 Calculate the square root of the right side: 2.178032865 Break this problem into two subproblems by setting (x + 1.277777778) equal to 2.178032865 and -2.178032865.Subproblem 1
x + 1.277777778 = 2.178032865 Simplifying x + 1.277777778 = 2.178032865 Reorder the terms: 1.277777778 + x = 2.178032865 Solving 1.277777778 + x = 2.178032865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = 2.178032865 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = 2.178032865 + -1.277777778 x = 2.178032865 + -1.277777778 Combine like terms: 2.178032865 + -1.277777778 = 0.900255087 x = 0.900255087 Simplifying x = 0.900255087Subproblem 2
x + 1.277777778 = -2.178032865 Simplifying x + 1.277777778 = -2.178032865 Reorder the terms: 1.277777778 + x = -2.178032865 Solving 1.277777778 + x = -2.178032865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = -2.178032865 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = -2.178032865 + -1.277777778 x = -2.178032865 + -1.277777778 Combine like terms: -2.178032865 + -1.277777778 = -3.455810643 x = -3.455810643 Simplifying x = -3.455810643Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.900255087, -3.455810643}
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