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Simplifying 3x(x + -14) + 1 = -4x + 5 Reorder the terms: 3x(-14 + x) + 1 = -4x + 5 (-14 * 3x + x * 3x) + 1 = -4x + 5 (-42x + 3x2) + 1 = -4x + 5 Reorder the terms: 1 + -42x + 3x2 = -4x + 5 Reorder the terms: 1 + -42x + 3x2 = 5 + -4x Solving 1 + -42x + 3x2 = 5 + -4x Solving for variable 'x'. Reorder the terms: 1 + -5 + -42x + 4x + 3x2 = 5 + -4x + -5 + 4x Combine like terms: 1 + -5 = -4 -4 + -42x + 4x + 3x2 = 5 + -4x + -5 + 4x Combine like terms: -42x + 4x = -38x -4 + -38x + 3x2 = 5 + -4x + -5 + 4x Reorder the terms: -4 + -38x + 3x2 = 5 + -5 + -4x + 4x Combine like terms: 5 + -5 = 0 -4 + -38x + 3x2 = 0 + -4x + 4x -4 + -38x + 3x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -4 + -38x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -12.66666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -12.66666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -12.66666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -12.66666667x + x2 = 0 + 1.333333333 -12.66666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -12.66666667x + x2 = 1.333333333 The x term is -12.66666667x. Take half its coefficient (-6.333333335). Square it (40.11111113) and add it to both sides. Add '40.11111113' to each side of the equation. -12.66666667x + 40.11111113 + x2 = 1.333333333 + 40.11111113 Reorder the terms: 40.11111113 + -12.66666667x + x2 = 1.333333333 + 40.11111113 Combine like terms: 1.333333333 + 40.11111113 = 41.444444463 40.11111113 + -12.66666667x + x2 = 41.444444463 Factor a perfect square on the left side: (x + -6.333333335)(x + -6.333333335) = 41.444444463 Calculate the square root of the right side: 6.437735973 Break this problem into two subproblems by setting (x + -6.333333335) equal to 6.437735973 and -6.437735973.Subproblem 1
x + -6.333333335 = 6.437735973 Simplifying x + -6.333333335 = 6.437735973 Reorder the terms: -6.333333335 + x = 6.437735973 Solving -6.333333335 + x = 6.437735973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + x = 6.437735973 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = 6.437735973 + 6.333333335 x = 6.437735973 + 6.333333335 Combine like terms: 6.437735973 + 6.333333335 = 12.771069308 x = 12.771069308 Simplifying x = 12.771069308Subproblem 2
x + -6.333333335 = -6.437735973 Simplifying x + -6.333333335 = -6.437735973 Reorder the terms: -6.333333335 + x = -6.437735973 Solving -6.333333335 + x = -6.437735973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + x = -6.437735973 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = -6.437735973 + 6.333333335 x = -6.437735973 + 6.333333335 Combine like terms: -6.437735973 + 6.333333335 = -0.104402638 x = -0.104402638 Simplifying x = -0.104402638Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.771069308, -0.104402638}
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