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Simplifying 2x + -3x(5 + -1x) = 22 + 4x 2x + (5 * -3x + -1x * -3x) = 22 + 4x 2x + (-15x + 3x2) = 22 + 4x Combine like terms: 2x + -15x = -13x -13x + 3x2 = 22 + 4x Solving -13x + 3x2 = 22 + 4x Solving for variable 'x'. Reorder the terms: -22 + -13x + -4x + 3x2 = 22 + 4x + -22 + -4x Combine like terms: -13x + -4x = -17x -22 + -17x + 3x2 = 22 + 4x + -22 + -4x Reorder the terms: -22 + -17x + 3x2 = 22 + -22 + 4x + -4x Combine like terms: 22 + -22 = 0 -22 + -17x + 3x2 = 0 + 4x + -4x -22 + -17x + 3x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -22 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7.333333333 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + -5.666666667x + 7.333333333 + x2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + -5.666666667x + x2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + -5.666666667x + x2 = 0 + 7.333333333 -5.666666667x + x2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 -5.666666667x + x2 = 7.333333333 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = 7.333333333 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 7.333333333 + 8.027777782 Combine like terms: 7.333333333 + 8.027777782 = 15.361111115 8.027777782 + -5.666666667x + x2 = 15.361111115 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 15.361111115 Calculate the square root of the right side: 3.919325339 Break this problem into two subproblems by setting (x + -2.833333334) equal to 3.919325339 and -3.919325339.Subproblem 1
x + -2.833333334 = 3.919325339 Simplifying x + -2.833333334 = 3.919325339 Reorder the terms: -2.833333334 + x = 3.919325339 Solving -2.833333334 + x = 3.919325339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 3.919325339 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 3.919325339 + 2.833333334 x = 3.919325339 + 2.833333334 Combine like terms: 3.919325339 + 2.833333334 = 6.752658673 x = 6.752658673 Simplifying x = 6.752658673Subproblem 2
x + -2.833333334 = -3.919325339 Simplifying x + -2.833333334 = -3.919325339 Reorder the terms: -2.833333334 + x = -3.919325339 Solving -2.833333334 + x = -3.919325339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -3.919325339 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -3.919325339 + 2.833333334 x = -3.919325339 + 2.833333334 Combine like terms: -3.919325339 + 2.833333334 = -1.085992005 x = -1.085992005 Simplifying x = -1.085992005Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.752658673, -1.085992005}
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