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Simplifying -4x + 5x(x + -2) = -16 + 10 Reorder the terms: -4x + 5x(-2 + x) = -16 + 10 -4x + (-2 * 5x + x * 5x) = -16 + 10 -4x + (-10x + 5x2) = -16 + 10 Combine like terms: -4x + -10x = -14x -14x + 5x2 = -16 + 10 Combine like terms: -16 + 10 = -6 -14x + 5x2 = -6 Solving -14x + 5x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + -14x + 5x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -2.8x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -2.8x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -2.8x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -2.8x + x2 = 0 + -1.2 -2.8x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -2.8x + x2 = -1.2 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = -1.2 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = -1.2 + 1.96 Combine like terms: -1.2 + 1.96 = 0.76 1.96 + -2.8x + x2 = 0.76 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (x + -1.4) equal to 0.871779789 and -0.871779789.Subproblem 1
x + -1.4 = 0.871779789 Simplifying x + -1.4 = 0.871779789 Reorder the terms: -1.4 + x = 0.871779789 Solving -1.4 + x = 0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 0.871779789 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 0.871779789 + 1.4 x = 0.871779789 + 1.4 Combine like terms: 0.871779789 + 1.4 = 2.271779789 x = 2.271779789 Simplifying x = 2.271779789Subproblem 2
x + -1.4 = -0.871779789 Simplifying x + -1.4 = -0.871779789 Reorder the terms: -1.4 + x = -0.871779789 Solving -1.4 + x = -0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -0.871779789 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -0.871779789 + 1.4 x = -0.871779789 + 1.4 Combine like terms: -0.871779789 + 1.4 = 0.528220211 x = 0.528220211 Simplifying x = 0.528220211Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.271779789, 0.528220211}
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