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Simplifying 3x(2x + -3) = x + 1 Reorder the terms: 3x(-3 + 2x) = x + 1 (-3 * 3x + 2x * 3x) = x + 1 (-9x + 6x2) = x + 1 Reorder the terms: -9x + 6x2 = 1 + x Solving -9x + 6x2 = 1 + x Solving for variable 'x'. Reorder the terms: -1 + -9x + -1x + 6x2 = 1 + x + -1 + -1x Combine like terms: -9x + -1x = -10x -1 + -10x + 6x2 = 1 + x + -1 + -1x Reorder the terms: -1 + -10x + 6x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 -1 + -10x + 6x2 = 0 + x + -1x -1 + -10x + 6x2 = x + -1x Combine like terms: x + -1x = 0 -1 + -10x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -1.666666667x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -1.666666667x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -1.666666667x + x2 = 0 + 0.1666666667 -1.666666667x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -1.666666667x + x2 = 0.1666666667 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 0.1666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 0.1666666667 + 0.6944444447 Combine like terms: 0.1666666667 + 0.6944444447 = 0.8611111114 0.6944444447 + -1.666666667x + x2 = 0.8611111114 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.8611111114 Calculate the square root of the right side: 0.927960727 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.927960727 and -0.927960727.Subproblem 1
x + -0.8333333335 = 0.927960727 Simplifying x + -0.8333333335 = 0.927960727 Reorder the terms: -0.8333333335 + x = 0.927960727 Solving -0.8333333335 + x = 0.927960727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 0.927960727 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.927960727 + 0.8333333335 x = 0.927960727 + 0.8333333335 Combine like terms: 0.927960727 + 0.8333333335 = 1.7612940605 x = 1.7612940605 Simplifying x = 1.7612940605Subproblem 2
x + -0.8333333335 = -0.927960727 Simplifying x + -0.8333333335 = -0.927960727 Reorder the terms: -0.8333333335 + x = -0.927960727 Solving -0.8333333335 + x = -0.927960727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -0.927960727 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.927960727 + 0.8333333335 x = -0.927960727 + 0.8333333335 Combine like terms: -0.927960727 + 0.8333333335 = -0.0946273935 x = -0.0946273935 Simplifying x = -0.0946273935Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7612940605, -0.0946273935}
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