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Simplifying 1.5x2 + -24x = 24 Reorder the terms: -24x + 1.5x2 = 24 Solving -24x + 1.5x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + -24x + 1.5x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -24x + 1.5x2 = 0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -16 + -16x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -16x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -16x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -16x + x2 = 0 + 16 -16x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -16x + x2 = 16 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 16 + 64 Reorder the terms: 64 + -16x + x2 = 16 + 64 Combine like terms: 16 + 64 = 80 64 + -16x + x2 = 80 Factor a perfect square on the left side: (x + -8)(x + -8) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -8) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -8 = 8.94427191 Simplifying x + -8 = 8.94427191 Reorder the terms: -8 + x = 8.94427191 Solving -8 + x = 8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 8.94427191 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.94427191 + 8 x = 8.94427191 + 8 Combine like terms: 8.94427191 + 8 = 16.94427191 x = 16.94427191 Simplifying x = 16.94427191Subproblem 2
x + -8 = -8.94427191 Simplifying x + -8 = -8.94427191 Reorder the terms: -8 + x = -8.94427191 Solving -8 + x = -8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -8.94427191 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.94427191 + 8 x = -8.94427191 + 8 Combine like terms: -8.94427191 + 8 = -0.94427191 x = -0.94427191 Simplifying x = -0.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.94427191, -0.94427191}
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