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Simplifying 1.5x(2x + -4) = 1.5x + 3 Reorder the terms: 1.5x(-4 + 2x) = 1.5x + 3 (-4 * 1.5x + 2x * 1.5x) = 1.5x + 3 (-6x + 3x2) = 1.5x + 3 Reorder the terms: -6x + 3x2 = 3 + 1.5x Solving -6x + 3x2 = 3 + 1.5x Solving for variable 'x'. Reorder the terms: -3 + -6x + -1.5x + 3x2 = 3 + 1.5x + -3 + -1.5x Combine like terms: -6x + -1.5x = -7.5x -3 + -7.5x + 3x2 = 3 + 1.5x + -3 + -1.5x Reorder the terms: -3 + -7.5x + 3x2 = 3 + -3 + 1.5x + -1.5x Combine like terms: 3 + -3 = 0 -3 + -7.5x + 3x2 = 0 + 1.5x + -1.5x -3 + -7.5x + 3x2 = 1.5x + -1.5x Combine like terms: 1.5x + -1.5x = 0.0 -3 + -7.5x + 3x2 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -2.5x + x2 = 0.0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.5x + 1 + x2 = 0.0 + 1 Reorder the terms: -1 + 1 + -2.5x + x2 = 0.0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.5x + x2 = 0.0 + 1 -2.5x + x2 = 0.0 + 1 Combine like terms: 0.0 + 1 = 1 -2.5x + x2 = 1 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1 + 1.5625 Combine like terms: 1 + 1.5625 = 2.5625 1.5625 + -2.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -1.25) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -1.25 = 1.600781059 Simplifying x + -1.25 = 1.600781059 Reorder the terms: -1.25 + x = 1.600781059 Solving -1.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.600781059 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.600781059 + 1.25 x = 1.600781059 + 1.25 Combine like terms: 1.600781059 + 1.25 = 2.850781059 x = 2.850781059 Simplifying x = 2.850781059Subproblem 2
x + -1.25 = -1.600781059 Simplifying x + -1.25 = -1.600781059 Reorder the terms: -1.25 + x = -1.600781059 Solving -1.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.600781059 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.600781059 + 1.25 x = -1.600781059 + 1.25 Combine like terms: -1.600781059 + 1.25 = -0.350781059 x = -0.350781059 Simplifying x = -0.350781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.850781059, -0.350781059}
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