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Simplifying (-5x + -4) + -1(-2 + -5x) * x = 3 Reorder the terms: (-4 + -5x) + -1(-2 + -5x) * x = 3 Remove parenthesis around (-4 + -5x) -4 + -5x + -1(-2 + -5x) * x = 3 Reorder the terms for easier multiplication: -4 + -5x + -1x(-2 + -5x) = 3 -4 + -5x + (-2 * -1x + -5x * -1x) = 3 -4 + -5x + (2x + 5x2) = 3 Combine like terms: -5x + 2x = -3x -4 + -3x + 5x2 = 3 Solving -4 + -3x + 5x2 = 3 Solving for variable 'x'. Reorder the terms: -4 + -3 + -3x + 5x2 = 3 + -3 Combine like terms: -4 + -3 = -7 -7 + -3x + 5x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -7 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -0.6x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.6x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.6x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.6x + x2 = 0 + 1.4 -0.6x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.6x + x2 = 1.4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 1.4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1.4 + 0.09 Combine like terms: 1.4 + 0.09 = 1.49 0.09 + -0.6x + x2 = 1.49 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (x + -0.3) equal to 1.220655562 and -1.220655562.Subproblem 1
x + -0.3 = 1.220655562 Simplifying x + -0.3 = 1.220655562 Reorder the terms: -0.3 + x = 1.220655562 Solving -0.3 + x = 1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.220655562 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.220655562 + 0.3 x = 1.220655562 + 0.3 Combine like terms: 1.220655562 + 0.3 = 1.520655562 x = 1.520655562 Simplifying x = 1.520655562Subproblem 2
x + -0.3 = -1.220655562 Simplifying x + -0.3 = -1.220655562 Reorder the terms: -0.3 + x = -1.220655562 Solving -0.3 + x = -1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.220655562 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.220655562 + 0.3 x = -1.220655562 + 0.3 Combine like terms: -1.220655562 + 0.3 = -0.920655562 x = -0.920655562 Simplifying x = -0.920655562Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.520655562, -0.920655562}
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