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Simplifying 5x(5x + 8x + -7) = 7x + -2 Reorder the terms: 5x(-7 + 5x + 8x) = 7x + -2 Combine like terms: 5x + 8x = 13x 5x(-7 + 13x) = 7x + -2 (-7 * 5x + 13x * 5x) = 7x + -2 (-35x + 65x2) = 7x + -2 Reorder the terms: -35x + 65x2 = -2 + 7x Solving -35x + 65x2 = -2 + 7x Solving for variable 'x'. Reorder the terms: 2 + -35x + -7x + 65x2 = -2 + 7x + 2 + -7x Combine like terms: -35x + -7x = -42x 2 + -42x + 65x2 = -2 + 7x + 2 + -7x Reorder the terms: 2 + -42x + 65x2 = -2 + 2 + 7x + -7x Combine like terms: -2 + 2 = 0 2 + -42x + 65x2 = 0 + 7x + -7x 2 + -42x + 65x2 = 7x + -7x Combine like terms: 7x + -7x = 0 2 + -42x + 65x2 = 0 Begin completing the square. Divide all terms by 65 the coefficient of the squared term: Divide each side by '65'. 0.03076923077 + -0.6461538462x + x2 = 0 Move the constant term to the right: Add '-0.03076923077' to each side of the equation. 0.03076923077 + -0.6461538462x + -0.03076923077 + x2 = 0 + -0.03076923077 Reorder the terms: 0.03076923077 + -0.03076923077 + -0.6461538462x + x2 = 0 + -0.03076923077 Combine like terms: 0.03076923077 + -0.03076923077 = 0.00000000000 0.00000000000 + -0.6461538462x + x2 = 0 + -0.03076923077 -0.6461538462x + x2 = 0 + -0.03076923077 Combine like terms: 0 + -0.03076923077 = -0.03076923077 -0.6461538462x + x2 = -0.03076923077 The x term is -0.6461538462x. Take half its coefficient (-0.3230769231). Square it (0.1043786982) and add it to both sides. Add '0.1043786982' to each side of the equation. -0.6461538462x + 0.1043786982 + x2 = -0.03076923077 + 0.1043786982 Reorder the terms: 0.1043786982 + -0.6461538462x + x2 = -0.03076923077 + 0.1043786982 Combine like terms: -0.03076923077 + 0.1043786982 = 0.07360946743 0.1043786982 + -0.6461538462x + x2 = 0.07360946743 Factor a perfect square on the left side: (x + -0.3230769231)(x + -0.3230769231) = 0.07360946743 Calculate the square root of the right side: 0.271310647 Break this problem into two subproblems by setting (x + -0.3230769231) equal to 0.271310647 and -0.271310647.Subproblem 1
x + -0.3230769231 = 0.271310647 Simplifying x + -0.3230769231 = 0.271310647 Reorder the terms: -0.3230769231 + x = 0.271310647 Solving -0.3230769231 + x = 0.271310647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3230769231' to each side of the equation. -0.3230769231 + 0.3230769231 + x = 0.271310647 + 0.3230769231 Combine like terms: -0.3230769231 + 0.3230769231 = 0.0000000000 0.0000000000 + x = 0.271310647 + 0.3230769231 x = 0.271310647 + 0.3230769231 Combine like terms: 0.271310647 + 0.3230769231 = 0.5943875701 x = 0.5943875701 Simplifying x = 0.5943875701Subproblem 2
x + -0.3230769231 = -0.271310647 Simplifying x + -0.3230769231 = -0.271310647 Reorder the terms: -0.3230769231 + x = -0.271310647 Solving -0.3230769231 + x = -0.271310647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3230769231' to each side of the equation. -0.3230769231 + 0.3230769231 + x = -0.271310647 + 0.3230769231 Combine like terms: -0.3230769231 + 0.3230769231 = 0.0000000000 0.0000000000 + x = -0.271310647 + 0.3230769231 x = -0.271310647 + 0.3230769231 Combine like terms: -0.271310647 + 0.3230769231 = 0.0517662761 x = 0.0517662761 Simplifying x = 0.0517662761Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5943875701, 0.0517662761}
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