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Simplifying 3 + -1(4x + 6) = 7 + -5x(x + 4) Reorder the terms: 3 + -1(6 + 4x) = 7 + -5x(x + 4) 3 + (6 * -1 + 4x * -1) = 7 + -5x(x + 4) 3 + (-6 + -4x) = 7 + -5x(x + 4) Combine like terms: 3 + -6 = -3 -3 + -4x = 7 + -5x(x + 4) Reorder the terms: -3 + -4x = 7 + -5x(4 + x) -3 + -4x = 7 + (4 * -5x + x * -5x) -3 + -4x = 7 + (-20x + -5x2) Solving -3 + -4x = 7 + -20x + -5x2 Solving for variable 'x'. Reorder the terms: -3 + -7 + -4x + 20x + 5x2 = 7 + -20x + -5x2 + -7 + 20x + 5x2 Combine like terms: -3 + -7 = -10 -10 + -4x + 20x + 5x2 = 7 + -20x + -5x2 + -7 + 20x + 5x2 Combine like terms: -4x + 20x = 16x -10 + 16x + 5x2 = 7 + -20x + -5x2 + -7 + 20x + 5x2 Reorder the terms: -10 + 16x + 5x2 = 7 + -7 + -20x + 20x + -5x2 + 5x2 Combine like terms: 7 + -7 = 0 -10 + 16x + 5x2 = 0 + -20x + 20x + -5x2 + 5x2 -10 + 16x + 5x2 = -20x + 20x + -5x2 + 5x2 Combine like terms: -20x + 20x = 0 -10 + 16x + 5x2 = 0 + -5x2 + 5x2 -10 + 16x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -10 + 16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + 3.2x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 3.2x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 3.2x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3.2x + x2 = 0 + 2 3.2x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 3.2x + x2 = 2 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = 2 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 2 + 2.56 Combine like terms: 2 + 2.56 = 4.56 2.56 + 3.2x + x2 = 4.56 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 4.56 Calculate the square root of the right side: 2.13541565 Break this problem into two subproblems by setting (x + 1.6) equal to 2.13541565 and -2.13541565.Subproblem 1
x + 1.6 = 2.13541565 Simplifying x + 1.6 = 2.13541565 Reorder the terms: 1.6 + x = 2.13541565 Solving 1.6 + x = 2.13541565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 2.13541565 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 2.13541565 + -1.6 x = 2.13541565 + -1.6 Combine like terms: 2.13541565 + -1.6 = 0.53541565 x = 0.53541565 Simplifying x = 0.53541565Subproblem 2
x + 1.6 = -2.13541565 Simplifying x + 1.6 = -2.13541565 Reorder the terms: 1.6 + x = -2.13541565 Solving 1.6 + x = -2.13541565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -2.13541565 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -2.13541565 + -1.6 x = -2.13541565 + -1.6 Combine like terms: -2.13541565 + -1.6 = -3.73541565 x = -3.73541565 Simplifying x = -3.73541565Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.53541565, -3.73541565}
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