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Simplifying 7x(1 + -1x) = 5x + -10 (1 * 7x + -1x * 7x) = 5x + -10 (7x + -7x2) = 5x + -10 Reorder the terms: 7x + -7x2 = -10 + 5x Solving 7x + -7x2 = -10 + 5x Solving for variable 'x'. Reorder the terms: 10 + 7x + -5x + -7x2 = -10 + 5x + 10 + -5x Combine like terms: 7x + -5x = 2x 10 + 2x + -7x2 = -10 + 5x + 10 + -5x Reorder the terms: 10 + 2x + -7x2 = -10 + 10 + 5x + -5x Combine like terms: -10 + 10 = 0 10 + 2x + -7x2 = 0 + 5x + -5x 10 + 2x + -7x2 = 5x + -5x Combine like terms: 5x + -5x = 0 10 + 2x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.428571429 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -0.2857142857x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -0.2857142857x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -0.2857142857x + x2 = 0 + 1.428571429 -0.2857142857x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -0.2857142857x + x2 = 1.428571429 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 1.428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 1.428571429 + 0.02040816328 Combine like terms: 1.428571429 + 0.02040816328 = 1.44897959228 0.02040816328 + -0.2857142857x + x2 = 1.44897959228 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 1.44897959228 Calculate the square root of the right side: 1.203735682 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 1.203735682 and -1.203735682.Subproblem 1
x + -0.1428571429 = 1.203735682 Simplifying x + -0.1428571429 = 1.203735682 Reorder the terms: -0.1428571429 + x = 1.203735682 Solving -0.1428571429 + x = 1.203735682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 1.203735682 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.203735682 + 0.1428571429 x = 1.203735682 + 0.1428571429 Combine like terms: 1.203735682 + 0.1428571429 = 1.3465928249 x = 1.3465928249 Simplifying x = 1.3465928249Subproblem 2
x + -0.1428571429 = -1.203735682 Simplifying x + -0.1428571429 = -1.203735682 Reorder the terms: -0.1428571429 + x = -1.203735682 Solving -0.1428571429 + x = -1.203735682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -1.203735682 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.203735682 + 0.1428571429 x = -1.203735682 + 0.1428571429 Combine like terms: -1.203735682 + 0.1428571429 = -1.0608785391 x = -1.0608785391 Simplifying x = -1.0608785391Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3465928249, -1.0608785391}
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