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Simplifying -2x + -5 = 2 + -4x(x + -1) Reorder the terms: -5 + -2x = 2 + -4x(x + -1) Reorder the terms: -5 + -2x = 2 + -4x(-1 + x) -5 + -2x = 2 + (-1 * -4x + x * -4x) -5 + -2x = 2 + (4x + -4x2) Solving -5 + -2x = 2 + 4x + -4x2 Solving for variable 'x'. Reorder the terms: -5 + -2 + -2x + -4x + 4x2 = 2 + 4x + -4x2 + -2 + -4x + 4x2 Combine like terms: -5 + -2 = -7 -7 + -2x + -4x + 4x2 = 2 + 4x + -4x2 + -2 + -4x + 4x2 Combine like terms: -2x + -4x = -6x -7 + -6x + 4x2 = 2 + 4x + -4x2 + -2 + -4x + 4x2 Reorder the terms: -7 + -6x + 4x2 = 2 + -2 + 4x + -4x + -4x2 + 4x2 Combine like terms: 2 + -2 = 0 -7 + -6x + 4x2 = 0 + 4x + -4x + -4x2 + 4x2 -7 + -6x + 4x2 = 4x + -4x + -4x2 + 4x2 Combine like terms: 4x + -4x = 0 -7 + -6x + 4x2 = 0 + -4x2 + 4x2 -7 + -6x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -7 + -6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -1.5x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -1.5x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -1.5x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -1.5x + x2 = 0 + 1.75 -1.5x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -1.5x + x2 = 1.75 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 1.75 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 1.75 + 0.5625 Combine like terms: 1.75 + 0.5625 = 2.3125 0.5625 + -1.5x + x2 = 2.3125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (x + -0.75) equal to 1.520690633 and -1.520690633.Subproblem 1
x + -0.75 = 1.520690633 Simplifying x + -0.75 = 1.520690633 Reorder the terms: -0.75 + x = 1.520690633 Solving -0.75 + x = 1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.520690633 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.520690633 + 0.75 x = 1.520690633 + 0.75 Combine like terms: 1.520690633 + 0.75 = 2.270690633 x = 2.270690633 Simplifying x = 2.270690633Subproblem 2
x + -0.75 = -1.520690633 Simplifying x + -0.75 = -1.520690633 Reorder the terms: -0.75 + x = -1.520690633 Solving -0.75 + x = -1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.520690633 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.520690633 + 0.75 x = -1.520690633 + 0.75 Combine like terms: -1.520690633 + 0.75 = -0.770690633 x = -0.770690633 Simplifying x = -0.770690633Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.270690633, -0.770690633}
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