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Simplifying 4(2x + 3) = -3x(x + -1) + 31 Reorder the terms: 4(3 + 2x) = -3x(x + -1) + 31 (3 * 4 + 2x * 4) = -3x(x + -1) + 31 (12 + 8x) = -3x(x + -1) + 31 Reorder the terms: 12 + 8x = -3x(-1 + x) + 31 12 + 8x = (-1 * -3x + x * -3x) + 31 12 + 8x = (3x + -3x2) + 31 Reorder the terms: 12 + 8x = 31 + 3x + -3x2 Solving 12 + 8x = 31 + 3x + -3x2 Solving for variable 'x'. Reorder the terms: 12 + -31 + 8x + -3x + 3x2 = 31 + 3x + -3x2 + -31 + -3x + 3x2 Combine like terms: 12 + -31 = -19 -19 + 8x + -3x + 3x2 = 31 + 3x + -3x2 + -31 + -3x + 3x2 Combine like terms: 8x + -3x = 5x -19 + 5x + 3x2 = 31 + 3x + -3x2 + -31 + -3x + 3x2 Reorder the terms: -19 + 5x + 3x2 = 31 + -31 + 3x + -3x + -3x2 + 3x2 Combine like terms: 31 + -31 = 0 -19 + 5x + 3x2 = 0 + 3x + -3x + -3x2 + 3x2 -19 + 5x + 3x2 = 3x + -3x + -3x2 + 3x2 Combine like terms: 3x + -3x = 0 -19 + 5x + 3x2 = 0 + -3x2 + 3x2 -19 + 5x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -19 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + 1.666666667x + 6.333333333 + x2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + 1.666666667x + x2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 6.333333333 1.666666667x + x2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 1.666666667x + x2 = 6.333333333 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 = 6.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 6.333333333 + 0.6944444447 Combine like terms: 6.333333333 + 0.6944444447 = 7.0277777777 0.6944444447 + 1.666666667x + x2 = 7.0277777777 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 7.0277777777 Calculate the square root of the right side: 2.65099562 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 2.65099562 and -2.65099562.Subproblem 1
x + 0.8333333335 = 2.65099562 Simplifying x + 0.8333333335 = 2.65099562 Reorder the terms: 0.8333333335 + x = 2.65099562 Solving 0.8333333335 + x = 2.65099562 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 = 2.65099562 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.65099562 + -0.8333333335 x = 2.65099562 + -0.8333333335 Combine like terms: 2.65099562 + -0.8333333335 = 1.8176622865 x = 1.8176622865 Simplifying x = 1.8176622865Subproblem 2
x + 0.8333333335 = -2.65099562 Simplifying x + 0.8333333335 = -2.65099562 Reorder the terms: 0.8333333335 + x = -2.65099562 Solving 0.8333333335 + x = -2.65099562 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 = -2.65099562 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.65099562 + -0.8333333335 x = -2.65099562 + -0.8333333335 Combine like terms: -2.65099562 + -0.8333333335 = -3.4843289535 x = -3.4843289535 Simplifying x = -3.4843289535Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8176622865, -3.4843289535}
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