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Simplifying 6[x(9x + -6)] = 4 + -5x Reorder the terms: 6[x(-6 + 9x)] = 4 + -5x 6[(-6 * x + 9x * x)] = 4 + -5x 6[(-6x + 9x2)] = 4 + -5x [-6x * 6 + 9x2 * 6] = 4 + -5x [-36x + 54x2] = 4 + -5x Solving -36x + 54x2 = 4 + -5x Solving for variable 'x'. Reorder the terms: -4 + -36x + 5x + 54x2 = 4 + -5x + -4 + 5x Combine like terms: -36x + 5x = -31x -4 + -31x + 54x2 = 4 + -5x + -4 + 5x Reorder the terms: -4 + -31x + 54x2 = 4 + -4 + -5x + 5x Combine like terms: 4 + -4 = 0 -4 + -31x + 54x2 = 0 + -5x + 5x -4 + -31x + 54x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -4 + -31x + 54x2 = 0 Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. -0.07407407407 + -0.5740740741x + x2 = 0 Move the constant term to the right: Add '0.07407407407' to each side of the equation. -0.07407407407 + -0.5740740741x + 0.07407407407 + x2 = 0 + 0.07407407407 Reorder the terms: -0.07407407407 + 0.07407407407 + -0.5740740741x + x2 = 0 + 0.07407407407 Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000 0.00000000000 + -0.5740740741x + x2 = 0 + 0.07407407407 -0.5740740741x + x2 = 0 + 0.07407407407 Combine like terms: 0 + 0.07407407407 = 0.07407407407 -0.5740740741x + x2 = 0.07407407407 The x term is -0.5740740741x. Take half its coefficient (-0.2870370371). Square it (0.08239026067) and add it to both sides. Add '0.08239026067' to each side of the equation. -0.5740740741x + 0.08239026067 + x2 = 0.07407407407 + 0.08239026067 Reorder the terms: 0.08239026067 + -0.5740740741x + x2 = 0.07407407407 + 0.08239026067 Combine like terms: 0.07407407407 + 0.08239026067 = 0.15646433474 0.08239026067 + -0.5740740741x + x2 = 0.15646433474 Factor a perfect square on the left side: (x + -0.2870370371)(x + -0.2870370371) = 0.15646433474 Calculate the square root of the right side: 0.395555729 Break this problem into two subproblems by setting (x + -0.2870370371) equal to 0.395555729 and -0.395555729.Subproblem 1
x + -0.2870370371 = 0.395555729 Simplifying x + -0.2870370371 = 0.395555729 Reorder the terms: -0.2870370371 + x = 0.395555729 Solving -0.2870370371 + x = 0.395555729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2870370371' to each side of the equation. -0.2870370371 + 0.2870370371 + x = 0.395555729 + 0.2870370371 Combine like terms: -0.2870370371 + 0.2870370371 = 0.0000000000 0.0000000000 + x = 0.395555729 + 0.2870370371 x = 0.395555729 + 0.2870370371 Combine like terms: 0.395555729 + 0.2870370371 = 0.6825927661 x = 0.6825927661 Simplifying x = 0.6825927661Subproblem 2
x + -0.2870370371 = -0.395555729 Simplifying x + -0.2870370371 = -0.395555729 Reorder the terms: -0.2870370371 + x = -0.395555729 Solving -0.2870370371 + x = -0.395555729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2870370371' to each side of the equation. -0.2870370371 + 0.2870370371 + x = -0.395555729 + 0.2870370371 Combine like terms: -0.2870370371 + 0.2870370371 = 0.0000000000 0.0000000000 + x = -0.395555729 + 0.2870370371 x = -0.395555729 + 0.2870370371 Combine like terms: -0.395555729 + 0.2870370371 = -0.1085186919 x = -0.1085186919 Simplifying x = -0.1085186919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6825927661, -0.1085186919}
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