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Simplifying 3x(2x + -3) + -1x = 31 Reorder the terms: 3x(-3 + 2x) + -1x = 31 (-3 * 3x + 2x * 3x) + -1x = 31 (-9x + 6x2) + -1x = 31 Reorder the terms: -9x + -1x + 6x2 = 31 Combine like terms: -9x + -1x = -10x -10x + 6x2 = 31 Solving -10x + 6x2 = 31 Solving for variable 'x'. Reorder the terms: -31 + -10x + 6x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + -10x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.166666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '5.166666667' to each side of the equation. -5.166666667 + -1.666666667x + 5.166666667 + x2 = 0 + 5.166666667 Reorder the terms: -5.166666667 + 5.166666667 + -1.666666667x + x2 = 0 + 5.166666667 Combine like terms: -5.166666667 + 5.166666667 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 5.166666667 -1.666666667x + x2 = 0 + 5.166666667 Combine like terms: 0 + 5.166666667 = 5.166666667 -1.666666667x + x2 = 5.166666667 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 = 5.166666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 5.166666667 + 0.6944444447 Combine like terms: 5.166666667 + 0.6944444447 = 5.8611111117 0.6944444447 + -1.666666667x + x2 = 5.8611111117 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 5.8611111117 Calculate the square root of the right side: 2.420973175 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 2.420973175 and -2.420973175.Subproblem 1
x + -0.8333333335 = 2.420973175 Simplifying x + -0.8333333335 = 2.420973175 Reorder the terms: -0.8333333335 + x = 2.420973175 Solving -0.8333333335 + x = 2.420973175 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 = 2.420973175 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 2.420973175 + 0.8333333335 x = 2.420973175 + 0.8333333335 Combine like terms: 2.420973175 + 0.8333333335 = 3.2543065085 x = 3.2543065085 Simplifying x = 3.2543065085Subproblem 2
x + -0.8333333335 = -2.420973175 Simplifying x + -0.8333333335 = -2.420973175 Reorder the terms: -0.8333333335 + x = -2.420973175 Solving -0.8333333335 + x = -2.420973175 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 = -2.420973175 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -2.420973175 + 0.8333333335 x = -2.420973175 + 0.8333333335 Combine like terms: -2.420973175 + 0.8333333335 = -1.5876398415 x = -1.5876398415 Simplifying x = -1.5876398415Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2543065085, -1.5876398415}
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