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Simplifying 9x(3x + -4) = -1(x + -8) Reorder the terms: 9x(-4 + 3x) = -1(x + -8) (-4 * 9x + 3x * 9x) = -1(x + -8) (-36x + 27x2) = -1(x + -8) Reorder the terms: -36x + 27x2 = -1(-8 + x) -36x + 27x2 = (-8 * -1 + x * -1) -36x + 27x2 = (8 + -1x) Solving -36x + 27x2 = 8 + -1x Solving for variable 'x'. Reorder the terms: -8 + -36x + x + 27x2 = 8 + -1x + -8 + x Combine like terms: -36x + x = -35x -8 + -35x + 27x2 = 8 + -1x + -8 + x Reorder the terms: -8 + -35x + 27x2 = 8 + -8 + -1x + x Combine like terms: 8 + -8 = 0 -8 + -35x + 27x2 = 0 + -1x + x -8 + -35x + 27x2 = -1x + x Combine like terms: -1x + x = 0 -8 + -35x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.2962962963 + -1.296296296x + x2 = 0 Move the constant term to the right: Add '0.2962962963' to each side of the equation. -0.2962962963 + -1.296296296x + 0.2962962963 + x2 = 0 + 0.2962962963 Reorder the terms: -0.2962962963 + 0.2962962963 + -1.296296296x + x2 = 0 + 0.2962962963 Combine like terms: -0.2962962963 + 0.2962962963 = 0.0000000000 0.0000000000 + -1.296296296x + x2 = 0 + 0.2962962963 -1.296296296x + x2 = 0 + 0.2962962963 Combine like terms: 0 + 0.2962962963 = 0.2962962963 -1.296296296x + x2 = 0.2962962963 The x term is -1.296296296x. Take half its coefficient (-0.648148148). Square it (0.4200960218) and add it to both sides. Add '0.4200960218' to each side of the equation. -1.296296296x + 0.4200960218 + x2 = 0.2962962963 + 0.4200960218 Reorder the terms: 0.4200960218 + -1.296296296x + x2 = 0.2962962963 + 0.4200960218 Combine like terms: 0.2962962963 + 0.4200960218 = 0.7163923181 0.4200960218 + -1.296296296x + x2 = 0.7163923181 Factor a perfect square on the left side: (x + -0.648148148)(x + -0.648148148) = 0.7163923181 Calculate the square root of the right side: 0.846399621 Break this problem into two subproblems by setting (x + -0.648148148) equal to 0.846399621 and -0.846399621.Subproblem 1
x + -0.648148148 = 0.846399621 Simplifying x + -0.648148148 = 0.846399621 Reorder the terms: -0.648148148 + x = 0.846399621 Solving -0.648148148 + x = 0.846399621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.648148148' to each side of the equation. -0.648148148 + 0.648148148 + x = 0.846399621 + 0.648148148 Combine like terms: -0.648148148 + 0.648148148 = 0.000000000 0.000000000 + x = 0.846399621 + 0.648148148 x = 0.846399621 + 0.648148148 Combine like terms: 0.846399621 + 0.648148148 = 1.494547769 x = 1.494547769 Simplifying x = 1.494547769Subproblem 2
x + -0.648148148 = -0.846399621 Simplifying x + -0.648148148 = -0.846399621 Reorder the terms: -0.648148148 + x = -0.846399621 Solving -0.648148148 + x = -0.846399621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.648148148' to each side of the equation. -0.648148148 + 0.648148148 + x = -0.846399621 + 0.648148148 Combine like terms: -0.648148148 + 0.648148148 = 0.000000000 0.000000000 + x = -0.846399621 + 0.648148148 x = -0.846399621 + 0.648148148 Combine like terms: -0.846399621 + 0.648148148 = -0.198251473 x = -0.198251473 Simplifying x = -0.198251473Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.494547769, -0.198251473}
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