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Simplifying 2x(6x + -7) = 4x + 8 + -3 Reorder the terms: 2x(-7 + 6x) = 4x + 8 + -3 (-7 * 2x + 6x * 2x) = 4x + 8 + -3 (-14x + 12x2) = 4x + 8 + -3 Reorder the terms: -14x + 12x2 = 8 + -3 + 4x Combine like terms: 8 + -3 = 5 -14x + 12x2 = 5 + 4x Solving -14x + 12x2 = 5 + 4x Solving for variable 'x'. Reorder the terms: -5 + -14x + -4x + 12x2 = 5 + 4x + -5 + -4x Combine like terms: -14x + -4x = -18x -5 + -18x + 12x2 = 5 + 4x + -5 + -4x Reorder the terms: -5 + -18x + 12x2 = 5 + -5 + 4x + -4x Combine like terms: 5 + -5 = 0 -5 + -18x + 12x2 = 0 + 4x + -4x -5 + -18x + 12x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -5 + -18x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -1.5x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -1.5x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + 0.4166666667 -1.5x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -1.5x + x2 = 0.4166666667 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.4166666667 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.4166666667 + 0.5625 Combine like terms: 0.4166666667 + 0.5625 = 0.9791666667 0.5625 + -1.5x + x2 = 0.9791666667 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.9791666667 Calculate the square root of the right side: 0.989528507 Break this problem into two subproblems by setting (x + -0.75) equal to 0.989528507 and -0.989528507.Subproblem 1
x + -0.75 = 0.989528507 Simplifying x + -0.75 = 0.989528507 Reorder the terms: -0.75 + x = 0.989528507 Solving -0.75 + x = 0.989528507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.989528507 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.989528507 + 0.75 x = 0.989528507 + 0.75 Combine like terms: 0.989528507 + 0.75 = 1.739528507 x = 1.739528507 Simplifying x = 1.739528507Subproblem 2
x + -0.75 = -0.989528507 Simplifying x + -0.75 = -0.989528507 Reorder the terms: -0.75 + x = -0.989528507 Solving -0.75 + x = -0.989528507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.989528507 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.989528507 + 0.75 x = -0.989528507 + 0.75 Combine like terms: -0.989528507 + 0.75 = -0.239528507 x = -0.239528507 Simplifying x = -0.239528507Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.739528507, -0.239528507}
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