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Simplifying 4x + -2x(3x + -7) = 6(2x + -7) + 5x Reorder the terms: 4x + -2x(-7 + 3x) = 6(2x + -7) + 5x 4x + (-7 * -2x + 3x * -2x) = 6(2x + -7) + 5x 4x + (14x + -6x2) = 6(2x + -7) + 5x Combine like terms: 4x + 14x = 18x 18x + -6x2 = 6(2x + -7) + 5x Reorder the terms: 18x + -6x2 = 6(-7 + 2x) + 5x 18x + -6x2 = (-7 * 6 + 2x * 6) + 5x 18x + -6x2 = (-42 + 12x) + 5x Combine like terms: 12x + 5x = 17x 18x + -6x2 = -42 + 17x Solving 18x + -6x2 = -42 + 17x Solving for variable 'x'. Reorder the terms: 42 + 18x + -17x + -6x2 = -42 + 17x + 42 + -17x Combine like terms: 18x + -17x = 1x 42 + 1x + -6x2 = -42 + 17x + 42 + -17x Reorder the terms: 42 + 1x + -6x2 = -42 + 42 + 17x + -17x Combine like terms: -42 + 42 = 0 42 + 1x + -6x2 = 0 + 17x + -17x 42 + 1x + -6x2 = 17x + -17x Combine like terms: 17x + -17x = 0 42 + 1x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -7 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.1666666667x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -0.1666666667x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.1666666667x + x2 = 0 + 7 -0.1666666667x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.1666666667x + x2 = 7 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 7 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 7 + 0.006944444447 Combine like terms: 7 + 0.006944444447 = 7.006944444447 0.006944444447 + -0.1666666667x + x2 = 7.006944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 7.006944444447 Calculate the square root of the right side: 2.647063362 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 2.647063362 and -2.647063362.Subproblem 1
x + -0.08333333335 = 2.647063362 Simplifying x + -0.08333333335 = 2.647063362 Reorder the terms: -0.08333333335 + x = 2.647063362 Solving -0.08333333335 + x = 2.647063362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 2.647063362 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 2.647063362 + 0.08333333335 x = 2.647063362 + 0.08333333335 Combine like terms: 2.647063362 + 0.08333333335 = 2.73039669535 x = 2.73039669535 Simplifying x = 2.73039669535Subproblem 2
x + -0.08333333335 = -2.647063362 Simplifying x + -0.08333333335 = -2.647063362 Reorder the terms: -0.08333333335 + x = -2.647063362 Solving -0.08333333335 + x = -2.647063362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -2.647063362 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -2.647063362 + 0.08333333335 x = -2.647063362 + 0.08333333335 Combine like terms: -2.647063362 + 0.08333333335 = -2.56373002865 x = -2.56373002865 Simplifying x = -2.56373002865Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.73039669535, -2.56373002865}
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