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Simplifying x(2x + -3) = 4x + -1 Reorder the terms: x(-3 + 2x) = 4x + -1 (-3 * x + 2x * x) = 4x + -1 (-3x + 2x2) = 4x + -1 Reorder the terms: -3x + 2x2 = -1 + 4x Solving -3x + 2x2 = -1 + 4x Solving for variable 'x'. Reorder the terms: 1 + -3x + -4x + 2x2 = -1 + 4x + 1 + -4x Combine like terms: -3x + -4x = -7x 1 + -7x + 2x2 = -1 + 4x + 1 + -4x Reorder the terms: 1 + -7x + 2x2 = -1 + 1 + 4x + -4x Combine like terms: -1 + 1 = 0 1 + -7x + 2x2 = 0 + 4x + -4x 1 + -7x + 2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 1 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3.5x + x2 = 0 + -0.5 -3.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3.5x + x2 = -0.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -0.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -0.5 + 3.0625 Combine like terms: -0.5 + 3.0625 = 2.5625 3.0625 + -3.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -1.75) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -1.75 = 1.600781059 Simplifying x + -1.75 = 1.600781059 Reorder the terms: -1.75 + x = 1.600781059 Solving -1.75 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.600781059 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.600781059 + 1.75 x = 1.600781059 + 1.75 Combine like terms: 1.600781059 + 1.75 = 3.350781059 x = 3.350781059 Simplifying x = 3.350781059Subproblem 2
x + -1.75 = -1.600781059 Simplifying x + -1.75 = -1.600781059 Reorder the terms: -1.75 + x = -1.600781059 Solving -1.75 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.600781059 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.600781059 + 1.75 x = -1.600781059 + 1.75 Combine like terms: -1.600781059 + 1.75 = 0.149218941 x = 0.149218941 Simplifying x = 0.149218941Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.350781059, 0.149218941}
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