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Simplifying 2x(3 + -1x) + -4(x + 2) = 3x(2 + -3x) + 5 + 7x + -12 (3 * 2x + -1x * 2x) + -4(x + 2) = 3x(2 + -3x) + 5 + 7x + -12 (6x + -2x2) + -4(x + 2) = 3x(2 + -3x) + 5 + 7x + -12 Reorder the terms: 6x + -2x2 + -4(2 + x) = 3x(2 + -3x) + 5 + 7x + -12 6x + -2x2 + (2 * -4 + x * -4) = 3x(2 + -3x) + 5 + 7x + -12 6x + -2x2 + (-8 + -4x) = 3x(2 + -3x) + 5 + 7x + -12 Reorder the terms: -8 + 6x + -4x + -2x2 = 3x(2 + -3x) + 5 + 7x + -12 Combine like terms: 6x + -4x = 2x -8 + 2x + -2x2 = 3x(2 + -3x) + 5 + 7x + -12 -8 + 2x + -2x2 = (2 * 3x + -3x * 3x) + 5 + 7x + -12 -8 + 2x + -2x2 = (6x + -9x2) + 5 + 7x + -12 Reorder the terms: -8 + 2x + -2x2 = 5 + -12 + 6x + 7x + -9x2 Combine like terms: 5 + -12 = -7 -8 + 2x + -2x2 = -7 + 6x + 7x + -9x2 Combine like terms: 6x + 7x = 13x -8 + 2x + -2x2 = -7 + 13x + -9x2 Solving -8 + 2x + -2x2 = -7 + 13x + -9x2 Solving for variable 'x'. Reorder the terms: -8 + 7 + 2x + -13x + -2x2 + 9x2 = -7 + 13x + -9x2 + 7 + -13x + 9x2 Combine like terms: -8 + 7 = -1 -1 + 2x + -13x + -2x2 + 9x2 = -7 + 13x + -9x2 + 7 + -13x + 9x2 Combine like terms: 2x + -13x = -11x -1 + -11x + -2x2 + 9x2 = -7 + 13x + -9x2 + 7 + -13x + 9x2 Combine like terms: -2x2 + 9x2 = 7x2 -1 + -11x + 7x2 = -7 + 13x + -9x2 + 7 + -13x + 9x2 Reorder the terms: -1 + -11x + 7x2 = -7 + 7 + 13x + -13x + -9x2 + 9x2 Combine like terms: -7 + 7 = 0 -1 + -11x + 7x2 = 0 + 13x + -13x + -9x2 + 9x2 -1 + -11x + 7x2 = 13x + -13x + -9x2 + 9x2 Combine like terms: 13x + -13x = 0 -1 + -11x + 7x2 = 0 + -9x2 + 9x2 -1 + -11x + 7x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -1 + -11x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -1.571428571x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -1.571428571x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -1.571428571x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -1.571428571x + x2 = 0 + 0.1428571429 -1.571428571x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -1.571428571x + x2 = 0.1428571429 The x term is -1.571428571x. Take half its coefficient (-0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. -1.571428571x + 0.6173469384 + x2 = 0.1428571429 + 0.6173469384 Reorder the terms: 0.6173469384 + -1.571428571x + x2 = 0.1428571429 + 0.6173469384 Combine like terms: 0.1428571429 + 0.6173469384 = 0.7602040813 0.6173469384 + -1.571428571x + x2 = 0.7602040813 Factor a perfect square on the left side: (x + -0.7857142855)(x + -0.7857142855) = 0.7602040813 Calculate the square root of the right side: 0.87189683 Break this problem into two subproblems by setting (x + -0.7857142855) equal to 0.87189683 and -0.87189683.Subproblem 1
x + -0.7857142855 = 0.87189683 Simplifying x + -0.7857142855 = 0.87189683 Reorder the terms: -0.7857142855 + x = 0.87189683 Solving -0.7857142855 + x = 0.87189683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = 0.87189683 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = 0.87189683 + 0.7857142855 x = 0.87189683 + 0.7857142855 Combine like terms: 0.87189683 + 0.7857142855 = 1.6576111155 x = 1.6576111155 Simplifying x = 1.6576111155Subproblem 2
x + -0.7857142855 = -0.87189683 Simplifying x + -0.7857142855 = -0.87189683 Reorder the terms: -0.7857142855 + x = -0.87189683 Solving -0.7857142855 + x = -0.87189683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = -0.87189683 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = -0.87189683 + 0.7857142855 x = -0.87189683 + 0.7857142855 Combine like terms: -0.87189683 + 0.7857142855 = -0.0861825445 x = -0.0861825445 Simplifying x = -0.0861825445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6576111155, -0.0861825445}
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