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Simplifying 14 + -3x(2x + 1) = 5 + -4x Reorder the terms: 14 + -3x(1 + 2x) = 5 + -4x 14 + (1 * -3x + 2x * -3x) = 5 + -4x 14 + (-3x + -6x2) = 5 + -4x Solving 14 + -3x + -6x2 = 5 + -4x Solving for variable 'x'. Reorder the terms: 14 + -5 + -3x + 4x + -6x2 = 5 + -4x + -5 + 4x Combine like terms: 14 + -5 = 9 9 + -3x + 4x + -6x2 = 5 + -4x + -5 + 4x Combine like terms: -3x + 4x = 1x 9 + 1x + -6x2 = 5 + -4x + -5 + 4x Reorder the terms: 9 + 1x + -6x2 = 5 + -5 + -4x + 4x Combine like terms: 5 + -5 = 0 9 + 1x + -6x2 = 0 + -4x + 4x 9 + 1x + -6x2 = -4x + 4x Combine like terms: -4x + 4x = 0 9 + 1x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.5 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.1666666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.1666666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.1666666667x + x2 = 0 + 1.5 -0.1666666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.1666666667x + x2 = 1.5 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 = 1.5 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 1.5 + 0.006944444447 Combine like terms: 1.5 + 0.006944444447 = 1.506944444447 0.006944444447 + -0.1666666667x + x2 = 1.506944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 1.506944444447 Calculate the square root of the right side: 1.227576655 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 1.227576655 and -1.227576655.Subproblem 1
x + -0.08333333335 = 1.227576655 Simplifying x + -0.08333333335 = 1.227576655 Reorder the terms: -0.08333333335 + x = 1.227576655 Solving -0.08333333335 + x = 1.227576655 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 = 1.227576655 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 1.227576655 + 0.08333333335 x = 1.227576655 + 0.08333333335 Combine like terms: 1.227576655 + 0.08333333335 = 1.31090998835 x = 1.31090998835 Simplifying x = 1.31090998835Subproblem 2
x + -0.08333333335 = -1.227576655 Simplifying x + -0.08333333335 = -1.227576655 Reorder the terms: -0.08333333335 + x = -1.227576655 Solving -0.08333333335 + x = -1.227576655 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 = -1.227576655 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -1.227576655 + 0.08333333335 x = -1.227576655 + 0.08333333335 Combine like terms: -1.227576655 + 0.08333333335 = -1.14424332165 x = -1.14424332165 Simplifying x = -1.14424332165Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.31090998835, -1.14424332165}
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