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Simplifying -0.5x2 + 16x + -12 = 100 Reorder the terms: -12 + 16x + -0.5x2 = 100 Solving -12 + 16x + -0.5x2 = 100 Solving for variable 'x'. Reorder the terms: -12 + -100 + 16x + -0.5x2 = 100 + -100 Combine like terms: -12 + -100 = -112 -112 + 16x + -0.5x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -112 + 16x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 224 + -32x + x2 = 0 Move the constant term to the right: Add '-224' to each side of the equation. 224 + -32x + -224 + x2 = 0 + -224 Reorder the terms: 224 + -224 + -32x + x2 = 0 + -224 Combine like terms: 224 + -224 = 0 0 + -32x + x2 = 0 + -224 -32x + x2 = 0 + -224 Combine like terms: 0 + -224 = -224 -32x + x2 = -224 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 = -224 + 256 Reorder the terms: 256 + -32x + x2 = -224 + 256 Combine like terms: -224 + 256 = 32 256 + -32x + x2 = 32 Factor a perfect square on the left side: (x + -16)(x + -16) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + -16) equal to 5.656854249 and -5.656854249.Subproblem 1
x + -16 = 5.656854249 Simplifying x + -16 = 5.656854249 Reorder the terms: -16 + x = 5.656854249 Solving -16 + x = 5.656854249 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 = 5.656854249 + 16 Combine like terms: -16 + 16 = 0 0 + x = 5.656854249 + 16 x = 5.656854249 + 16 Combine like terms: 5.656854249 + 16 = 21.656854249 x = 21.656854249 Simplifying x = 21.656854249Subproblem 2
x + -16 = -5.656854249 Simplifying x + -16 = -5.656854249 Reorder the terms: -16 + x = -5.656854249 Solving -16 + x = -5.656854249 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 = -5.656854249 + 16 Combine like terms: -16 + 16 = 0 0 + x = -5.656854249 + 16 x = -5.656854249 + 16 Combine like terms: -5.656854249 + 16 = 10.343145751 x = 10.343145751 Simplifying x = 10.343145751Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.656854249, 10.343145751}
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