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Simplifying 2x(x + 4) = (x + -3)(x + -3) Reorder the terms: 2x(4 + x) = (x + -3)(x + -3) (4 * 2x + x * 2x) = (x + -3)(x + -3) (8x + 2x2) = (x + -3)(x + -3) Reorder the terms: 8x + 2x2 = (-3 + x)(x + -3) Reorder the terms: 8x + 2x2 = (-3 + x)(-3 + x) Multiply (-3 + x) * (-3 + x) 8x + 2x2 = (-3(-3 + x) + x(-3 + x)) 8x + 2x2 = ((-3 * -3 + x * -3) + x(-3 + x)) 8x + 2x2 = ((9 + -3x) + x(-3 + x)) 8x + 2x2 = (9 + -3x + (-3 * x + x * x)) 8x + 2x2 = (9 + -3x + (-3x + x2)) Combine like terms: -3x + -3x = -6x 8x + 2x2 = (9 + -6x + x2) Solving 8x + 2x2 = 9 + -6x + x2 Solving for variable 'x'. Reorder the terms: -9 + 8x + 6x + 2x2 + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Combine like terms: 8x + 6x = 14x -9 + 14x + 2x2 + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -9 + 14x + 1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Reorder the terms: -9 + 14x + 1x2 = 9 + -9 + -6x + 6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 -9 + 14x + 1x2 = 0 + -6x + 6x + x2 + -1x2 -9 + 14x + 1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -9 + 14x + 1x2 = 0 + x2 + -1x2 -9 + 14x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + 14x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 14x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 14x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 14x + x2 = 0 + 9 14x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 14x + x2 = 9 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 9 + 49 Reorder the terms: 49 + 14x + x2 = 9 + 49 Combine like terms: 9 + 49 = 58 49 + 14x + x2 = 58 Factor a perfect square on the left side: (x + 7)(x + 7) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + 7) equal to 7.615773106 and -7.615773106.Subproblem 1
x + 7 = 7.615773106 Simplifying x + 7 = 7.615773106 Reorder the terms: 7 + x = 7.615773106 Solving 7 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 7.615773106 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.615773106 + -7 x = 7.615773106 + -7 Combine like terms: 7.615773106 + -7 = 0.615773106 x = 0.615773106 Simplifying x = 0.615773106Subproblem 2
x + 7 = -7.615773106 Simplifying x + 7 = -7.615773106 Reorder the terms: 7 + x = -7.615773106 Solving 7 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -7.615773106 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.615773106 + -7 x = -7.615773106 + -7 Combine like terms: -7.615773106 + -7 = -14.615773106 x = -14.615773106 Simplifying x = -14.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.615773106, -14.615773106}
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