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Simplifying 3x(2x + -1) + 4(x + -2) = 0 Reorder the terms: 3x(-1 + 2x) + 4(x + -2) = 0 (-1 * 3x + 2x * 3x) + 4(x + -2) = 0 (-3x + 6x2) + 4(x + -2) = 0 Reorder the terms: -3x + 6x2 + 4(-2 + x) = 0 -3x + 6x2 + (-2 * 4 + x * 4) = 0 -3x + 6x2 + (-8 + 4x) = 0 Reorder the terms: -8 + -3x + 4x + 6x2 = 0 Combine like terms: -3x + 4x = 1x -8 + 1x + 6x2 = 0 Solving -8 + 1x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.333333333 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 0.1666666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 0.1666666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 0.1666666667x + x2 = 0 + 1.333333333 0.1666666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 0.1666666667x + x2 = 1.333333333 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 = 1.333333333 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 1.333333333 + 0.006944444447 Combine like terms: 1.333333333 + 0.006944444447 = 1.340277777447 0.006944444447 + 0.1666666667x + x2 = 1.340277777447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 1.340277777447 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 1.157703666 and -1.157703666.Subproblem 1
x + 0.08333333335 = 1.157703666 Simplifying x + 0.08333333335 = 1.157703666 Reorder the terms: 0.08333333335 + x = 1.157703666 Solving 0.08333333335 + x = 1.157703666 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 = 1.157703666 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 1.157703666 + -0.08333333335 x = 1.157703666 + -0.08333333335 Combine like terms: 1.157703666 + -0.08333333335 = 1.07437033265 x = 1.07437033265 Simplifying x = 1.07437033265Subproblem 2
x + 0.08333333335 = -1.157703666 Simplifying x + 0.08333333335 = -1.157703666 Reorder the terms: 0.08333333335 + x = -1.157703666 Solving 0.08333333335 + x = -1.157703666 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 = -1.157703666 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -1.157703666 + -0.08333333335 x = -1.157703666 + -0.08333333335 Combine like terms: -1.157703666 + -0.08333333335 = -1.24103699935 x = -1.24103699935 Simplifying x = -1.24103699935Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.07437033265, -1.24103699935}
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