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Simplifying (x + -4)(x + -2) = 4x(x + -3) Reorder the terms: (-4 + x)(x + -2) = 4x(x + -3) Reorder the terms: (-4 + x)(-2 + x) = 4x(x + -3) Multiply (-4 + x) * (-2 + x) (-4(-2 + x) + x(-2 + x)) = 4x(x + -3) ((-2 * -4 + x * -4) + x(-2 + x)) = 4x(x + -3) ((8 + -4x) + x(-2 + x)) = 4x(x + -3) (8 + -4x + (-2 * x + x * x)) = 4x(x + -3) (8 + -4x + (-2x + x2)) = 4x(x + -3) Combine like terms: -4x + -2x = -6x (8 + -6x + x2) = 4x(x + -3) Reorder the terms: 8 + -6x + x2 = 4x(-3 + x) 8 + -6x + x2 = (-3 * 4x + x * 4x) 8 + -6x + x2 = (-12x + 4x2) Solving 8 + -6x + x2 = -12x + 4x2 Solving for variable 'x'. Reorder the terms: 8 + -6x + 12x + x2 + -4x2 = -12x + 4x2 + 12x + -4x2 Combine like terms: -6x + 12x = 6x 8 + 6x + x2 + -4x2 = -12x + 4x2 + 12x + -4x2 Combine like terms: x2 + -4x2 = -3x2 8 + 6x + -3x2 = -12x + 4x2 + 12x + -4x2 Reorder the terms: 8 + 6x + -3x2 = -12x + 12x + 4x2 + -4x2 Combine like terms: -12x + 12x = 0 8 + 6x + -3x2 = 0 + 4x2 + -4x2 8 + 6x + -3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 8 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.666666667 + -2x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -2x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -2x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -2x + x2 = 0 + 2.666666667 -2x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -2x + x2 = 2.666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 2.666666667 + 1 Reorder the terms: 1 + -2x + x2 = 2.666666667 + 1 Combine like terms: 2.666666667 + 1 = 3.666666667 1 + -2x + x2 = 3.666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 3.666666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (x + -1) equal to 1.914854216 and -1.914854216.Subproblem 1
x + -1 = 1.914854216 Simplifying x + -1 = 1.914854216 Reorder the terms: -1 + x = 1.914854216 Solving -1 + x = 1.914854216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.914854216 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.914854216 + 1 x = 1.914854216 + 1 Combine like terms: 1.914854216 + 1 = 2.914854216 x = 2.914854216 Simplifying x = 2.914854216Subproblem 2
x + -1 = -1.914854216 Simplifying x + -1 = -1.914854216 Reorder the terms: -1 + x = -1.914854216 Solving -1 + x = -1.914854216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.914854216 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.914854216 + 1 x = -1.914854216 + 1 Combine like terms: -1.914854216 + 1 = -0.914854216 x = -0.914854216 Simplifying x = -0.914854216Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.914854216, -0.914854216}
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