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Simplifying x + 2(5x + -3) = x(7 + -1x) Reorder the terms: x + 2(-3 + 5x) = x(7 + -1x) x + (-3 * 2 + 5x * 2) = x(7 + -1x) x + (-6 + 10x) = x(7 + -1x) Reorder the terms: -6 + x + 10x = x(7 + -1x) Combine like terms: x + 10x = 11x -6 + 11x = x(7 + -1x) -6 + 11x = (7 * x + -1x * x) -6 + 11x = (7x + -1x2) Solving -6 + 11x = 7x + -1x2 Solving for variable 'x'. Combine like terms: 11x + -7x = 4x -6 + 4x + x2 = 7x + -1x2 + -7x + x2 Reorder the terms: -6 + 4x + x2 = 7x + -7x + -1x2 + x2 Combine like terms: 7x + -7x = 0 -6 + 4x + x2 = 0 + -1x2 + x2 -6 + 4x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -6 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4x + x2 = 0 + 6 4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 4x + x2 = 6 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 6 + 4 Reorder the terms: 4 + 4x + x2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + 4x + x2 = 10 Factor a perfect square on the left side: (x + 2)(x + 2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 2) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 2 = 3.16227766 Simplifying x + 2 = 3.16227766 Reorder the terms: 2 + x = 3.16227766 Solving 2 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.16227766 + -2 x = 3.16227766 + -2 Combine like terms: 3.16227766 + -2 = 1.16227766 x = 1.16227766 Simplifying x = 1.16227766Subproblem 2
x + 2 = -3.16227766 Simplifying x + 2 = -3.16227766 Reorder the terms: 2 + x = -3.16227766 Solving 2 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.16227766 + -2 x = -3.16227766 + -2 Combine like terms: -3.16227766 + -2 = -5.16227766 x = -5.16227766 Simplifying x = -5.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.16227766, -5.16227766}
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