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Simplifying (x2 + 4x + 4) + -1(4x2 + -8x + 5) = 0 Reorder the terms: (4 + 4x + x2) + -1(4x2 + -8x + 5) = 0 Remove parenthesis around (4 + 4x + x2) 4 + 4x + x2 + -1(4x2 + -8x + 5) = 0 Reorder the terms: 4 + 4x + x2 + -1(5 + -8x + 4x2) = 0 4 + 4x + x2 + (5 * -1 + -8x * -1 + 4x2 * -1) = 0 4 + 4x + x2 + (-5 + 8x + -4x2) = 0 Reorder the terms: 4 + -5 + 4x + 8x + x2 + -4x2 = 0 Combine like terms: 4 + -5 = -1 -1 + 4x + 8x + x2 + -4x2 = 0 Combine like terms: 4x + 8x = 12x -1 + 12x + x2 + -4x2 = 0 Combine like terms: x2 + -4x2 = -3x2 -1 + 12x + -3x2 = 0 Solving -1 + 12x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.3333333333 + -4x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -4x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -4x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.3333333333 -4x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -4x + x2 = -0.3333333333 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 = -0.3333333333 + 4 Reorder the terms: 4 + -4x + x2 = -0.3333333333 + 4 Combine like terms: -0.3333333333 + 4 = 3.6666666667 4 + -4x + x2 = 3.6666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.6666666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (x + -2) equal to 1.914854216 and -1.914854216.Subproblem 1
x + -2 = 1.914854216 Simplifying x + -2 = 1.914854216 Reorder the terms: -2 + x = 1.914854216 Solving -2 + x = 1.914854216 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 = 1.914854216 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.914854216 + 2 x = 1.914854216 + 2 Combine like terms: 1.914854216 + 2 = 3.914854216 x = 3.914854216 Simplifying x = 3.914854216Subproblem 2
x + -2 = -1.914854216 Simplifying x + -2 = -1.914854216 Reorder the terms: -2 + x = -1.914854216 Solving -2 + x = -1.914854216 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 = -1.914854216 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.914854216 + 2 x = -1.914854216 + 2 Combine like terms: -1.914854216 + 2 = 0.085145784 x = 0.085145784 Simplifying x = 0.085145784Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.914854216, 0.085145784}
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