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Simplifying 0 = -0.1x2 + 3.2x + -3.5 Reorder the terms: 0 = -3.5 + 3.2x + -0.1x2 Solving 0 = -3.5 + 3.2x + -0.1x2 Solving for variable 'x'. Combine like terms: 0 + 3.5 = 3.5 3.5 + -3.2x + 0.1x2 = -3.5 + 3.2x + -0.1x2 + 3.5 + -3.2x + 0.1x2 Reorder the terms: 3.5 + -3.2x + 0.1x2 = -3.5 + 3.5 + 3.2x + -3.2x + -0.1x2 + 0.1x2 Combine like terms: -3.5 + 3.5 = 0.0 3.5 + -3.2x + 0.1x2 = 0.0 + 3.2x + -3.2x + -0.1x2 + 0.1x2 3.5 + -3.2x + 0.1x2 = 3.2x + -3.2x + -0.1x2 + 0.1x2 Combine like terms: 3.2x + -3.2x = 0.0 3.5 + -3.2x + 0.1x2 = 0.0 + -0.1x2 + 0.1x2 3.5 + -3.2x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 3.5 + -3.2x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 35 + -32x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + -32x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -32x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -32x + x2 = 0 + -35 -32x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -32x + x2 = -35 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -35 + 256 Reorder the terms: 256 + -32x + x2 = -35 + 256 Combine like terms: -35 + 256 = 221 256 + -32x + x2 = 221 Factor a perfect square on the left side: (x + -16)(x + -16) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (x + -16) equal to 14.866068747 and -14.866068747.Subproblem 1
x + -16 = 14.866068747 Simplifying x + -16 = 14.866068747 Reorder the terms: -16 + x = 14.866068747 Solving -16 + x = 14.866068747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 14.866068747 + 16 Combine like terms: -16 + 16 = 0 0 + x = 14.866068747 + 16 x = 14.866068747 + 16 Combine like terms: 14.866068747 + 16 = 30.866068747 x = 30.866068747 Simplifying x = 30.866068747Subproblem 2
x + -16 = -14.866068747 Simplifying x + -16 = -14.866068747 Reorder the terms: -16 + x = -14.866068747 Solving -16 + x = -14.866068747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -14.866068747 + 16 Combine like terms: -16 + 16 = 0 0 + x = -14.866068747 + 16 x = -14.866068747 + 16 Combine like terms: -14.866068747 + 16 = 1.133931253 x = 1.133931253 Simplifying x = 1.133931253Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.866068747, 1.133931253}
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