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Simplifying 1.5x2 + -48x + 144 = 0 Reorder the terms: 144 + -48x + 1.5x2 = 0 Solving 144 + -48x + 1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 96 + -32x + x2 = 0 Move the constant term to the right: Add '-96' to each side of the equation. 96 + -32x + -96 + x2 = 0 + -96 Reorder the terms: 96 + -96 + -32x + x2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -32x + x2 = 0 + -96 -32x + x2 = 0 + -96 Combine like terms: 0 + -96 = -96 -32x + x2 = -96 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 = -96 + 256 Reorder the terms: 256 + -32x + x2 = -96 + 256 Combine like terms: -96 + 256 = 160 256 + -32x + x2 = 160 Factor a perfect square on the left side: (x + -16)(x + -16) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (x + -16) equal to 12.649110641 and -12.649110641.Subproblem 1
x + -16 = 12.649110641 Simplifying x + -16 = 12.649110641 Reorder the terms: -16 + x = 12.649110641 Solving -16 + x = 12.649110641 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 = 12.649110641 + 16 Combine like terms: -16 + 16 = 0 0 + x = 12.649110641 + 16 x = 12.649110641 + 16 Combine like terms: 12.649110641 + 16 = 28.649110641 x = 28.649110641 Simplifying x = 28.649110641Subproblem 2
x + -16 = -12.649110641 Simplifying x + -16 = -12.649110641 Reorder the terms: -16 + x = -12.649110641 Solving -16 + x = -12.649110641 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 = -12.649110641 + 16 Combine like terms: -16 + 16 = 0 0 + x = -12.649110641 + 16 x = -12.649110641 + 16 Combine like terms: -12.649110641 + 16 = 3.350889359 x = 3.350889359 Simplifying x = 3.350889359Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.649110641, 3.350889359}
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