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Simplifying 23 = 5 + 35x + -16x2 Solving 23 = 5 + 35x + -16x2 Solving for variable 'x'. Combine like terms: 23 + -5 = 18 18 + -35x + 16x2 = 5 + 35x + -16x2 + -5 + -35x + 16x2 Reorder the terms: 18 + -35x + 16x2 = 5 + -5 + 35x + -35x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 18 + -35x + 16x2 = 0 + 35x + -35x + -16x2 + 16x2 18 + -35x + 16x2 = 35x + -35x + -16x2 + 16x2 Combine like terms: 35x + -35x = 0 18 + -35x + 16x2 = 0 + -16x2 + 16x2 18 + -35x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 18 + -35x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.125 + -2.1875x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -2.1875x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -2.1875x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -2.1875x + x2 = 0 + -1.125 -2.1875x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -2.1875x + x2 = -1.125 The x term is -2.1875x. Take half its coefficient (-1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. -2.1875x + 1.196289063 + x2 = -1.125 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875x + x2 = -1.125 + 1.196289063 Combine like terms: -1.125 + 1.196289063 = 0.071289063 1.196289063 + -2.1875x + x2 = 0.071289063 Factor a perfect square on the left side: (x + -1.09375)(x + -1.09375) = 0.071289063 Calculate the square root of the right side: 0.267000118 Break this problem into two subproblems by setting (x + -1.09375) equal to 0.267000118 and -0.267000118.Subproblem 1
x + -1.09375 = 0.267000118 Simplifying x + -1.09375 = 0.267000118 Reorder the terms: -1.09375 + x = 0.267000118 Solving -1.09375 + x = 0.267000118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + x = 0.267000118 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = 0.267000118 + 1.09375 x = 0.267000118 + 1.09375 Combine like terms: 0.267000118 + 1.09375 = 1.360750118 x = 1.360750118 Simplifying x = 1.360750118Subproblem 2
x + -1.09375 = -0.267000118 Simplifying x + -1.09375 = -0.267000118 Reorder the terms: -1.09375 + x = -0.267000118 Solving -1.09375 + x = -0.267000118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + x = -0.267000118 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = -0.267000118 + 1.09375 x = -0.267000118 + 1.09375 Combine like terms: -0.267000118 + 1.09375 = 0.826749882 x = 0.826749882 Simplifying x = 0.826749882Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.360750118, 0.826749882}
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