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Simplifying x = 16x2 + -44x + 18 Reorder the terms: x = 18 + -44x + 16x2 Solving x = 18 + -44x + 16x2 Solving for variable 'x'. Reorder the terms: -18 + x + 44x + -16x2 = 18 + -44x + 16x2 + -18 + 44x + -16x2 Combine like terms: x + 44x = 45x -18 + 45x + -16x2 = 18 + -44x + 16x2 + -18 + 44x + -16x2 Reorder the terms: -18 + 45x + -16x2 = 18 + -18 + -44x + 44x + 16x2 + -16x2 Combine like terms: 18 + -18 = 0 -18 + 45x + -16x2 = 0 + -44x + 44x + 16x2 + -16x2 -18 + 45x + -16x2 = -44x + 44x + 16x2 + -16x2 Combine like terms: -44x + 44x = 0 -18 + 45x + -16x2 = 0 + 16x2 + -16x2 -18 + 45x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -18 + 45x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.125 + -2.8125x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -2.8125x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -2.8125x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -2.8125x + x2 = 0 + -1.125 -2.8125x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -2.8125x + x2 = -1.125 The x term is -2.8125x. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125x + 1.977539063 + x2 = -1.125 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125x + x2 = -1.125 + 1.977539063 Combine like terms: -1.125 + 1.977539063 = 0.852539063 1.977539063 + -2.8125x + x2 = 0.852539063 Factor a perfect square on the left side: (x + -1.40625)(x + -1.40625) = 0.852539063 Calculate the square root of the right side: 0.923330419 Break this problem into two subproblems by setting (x + -1.40625) equal to 0.923330419 and -0.923330419.Subproblem 1
x + -1.40625 = 0.923330419 Simplifying x + -1.40625 = 0.923330419 Reorder the terms: -1.40625 + x = 0.923330419 Solving -1.40625 + x = 0.923330419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + x = 0.923330419 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + x = 0.923330419 + 1.40625 x = 0.923330419 + 1.40625 Combine like terms: 0.923330419 + 1.40625 = 2.329580419 x = 2.329580419 Simplifying x = 2.329580419Subproblem 2
x + -1.40625 = -0.923330419 Simplifying x + -1.40625 = -0.923330419 Reorder the terms: -1.40625 + x = -0.923330419 Solving -1.40625 + x = -0.923330419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + x = -0.923330419 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + x = -0.923330419 + 1.40625 x = -0.923330419 + 1.40625 Combine like terms: -0.923330419 + 1.40625 = 0.482919581 x = 0.482919581 Simplifying x = 0.482919581Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.329580419, 0.482919581}
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