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Simplifying 3x(x + -4) = 4 + -1(4x + -5) Reorder the terms: 3x(-4 + x) = 4 + -1(4x + -5) (-4 * 3x + x * 3x) = 4 + -1(4x + -5) (-12x + 3x2) = 4 + -1(4x + -5) Reorder the terms: -12x + 3x2 = 4 + -1(-5 + 4x) -12x + 3x2 = 4 + (-5 * -1 + 4x * -1) -12x + 3x2 = 4 + (5 + -4x) Combine like terms: 4 + 5 = 9 -12x + 3x2 = 9 + -4x Solving -12x + 3x2 = 9 + -4x Solving for variable 'x'. Reorder the terms: -9 + -12x + 4x + 3x2 = 9 + -4x + -9 + 4x Combine like terms: -12x + 4x = -8x -9 + -8x + 3x2 = 9 + -4x + -9 + 4x Reorder the terms: -9 + -8x + 3x2 = 9 + -9 + -4x + 4x Combine like terms: 9 + -9 = 0 -9 + -8x + 3x2 = 0 + -4x + 4x -9 + -8x + 3x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -9 + -8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.666666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -2.666666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.666666667x + x2 = 0 + 3 -2.666666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.666666667x + x2 = 3 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 3 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 3 + 1.777777780 Combine like terms: 3 + 1.777777780 = 4.77777778 1.777777780 + -2.666666667x + x2 = 4.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 4.77777778 Calculate the square root of the right side: 2.185812842 Break this problem into two subproblems by setting (x + -1.333333334) equal to 2.185812842 and -2.185812842.Subproblem 1
x + -1.333333334 = 2.185812842 Simplifying x + -1.333333334 = 2.185812842 Reorder the terms: -1.333333334 + x = 2.185812842 Solving -1.333333334 + x = 2.185812842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 2.185812842 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.185812842 + 1.333333334 x = 2.185812842 + 1.333333334 Combine like terms: 2.185812842 + 1.333333334 = 3.519146176 x = 3.519146176 Simplifying x = 3.519146176Subproblem 2
x + -1.333333334 = -2.185812842 Simplifying x + -1.333333334 = -2.185812842 Reorder the terms: -1.333333334 + x = -2.185812842 Solving -1.333333334 + x = -2.185812842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -2.185812842 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.185812842 + 1.333333334 x = -2.185812842 + 1.333333334 Combine like terms: -2.185812842 + 1.333333334 = -0.852479508 x = -0.852479508 Simplifying x = -0.852479508Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.519146176, -0.852479508}
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