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Simplifying 3x(x + 7) = -17 + -2x Reorder the terms: 3x(7 + x) = -17 + -2x (7 * 3x + x * 3x) = -17 + -2x (21x + 3x2) = -17 + -2x Solving 21x + 3x2 = -17 + -2x Solving for variable 'x'. Reorder the terms: 17 + 21x + 2x + 3x2 = -17 + -2x + 17 + 2x Combine like terms: 21x + 2x = 23x 17 + 23x + 3x2 = -17 + -2x + 17 + 2x Reorder the terms: 17 + 23x + 3x2 = -17 + 17 + -2x + 2x Combine like terms: -17 + 17 = 0 17 + 23x + 3x2 = 0 + -2x + 2x 17 + 23x + 3x2 = -2x + 2x Combine like terms: -2x + 2x = 0 17 + 23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.666666667 + 7.666666667x + x2 = 0 Move the constant term to the right: Add '-5.666666667' to each side of the equation. 5.666666667 + 7.666666667x + -5.666666667 + x2 = 0 + -5.666666667 Reorder the terms: 5.666666667 + -5.666666667 + 7.666666667x + x2 = 0 + -5.666666667 Combine like terms: 5.666666667 + -5.666666667 = 0.000000000 0.000000000 + 7.666666667x + x2 = 0 + -5.666666667 7.666666667x + x2 = 0 + -5.666666667 Combine like terms: 0 + -5.666666667 = -5.666666667 7.666666667x + x2 = -5.666666667 The x term is 7.666666667x. Take half its coefficient (3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. 7.666666667x + 14.69444445 + x2 = -5.666666667 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667x + x2 = -5.666666667 + 14.69444445 Combine like terms: -5.666666667 + 14.69444445 = 9.027777783 14.69444445 + 7.666666667x + x2 = 9.027777783 Factor a perfect square on the left side: (x + 3.833333334)(x + 3.833333334) = 9.027777783 Calculate the square root of the right side: 3.004626064 Break this problem into two subproblems by setting (x + 3.833333334) equal to 3.004626064 and -3.004626064.Subproblem 1
x + 3.833333334 = 3.004626064 Simplifying x + 3.833333334 = 3.004626064 Reorder the terms: 3.833333334 + x = 3.004626064 Solving 3.833333334 + x = 3.004626064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + x = 3.004626064 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = 3.004626064 + -3.833333334 x = 3.004626064 + -3.833333334 Combine like terms: 3.004626064 + -3.833333334 = -0.82870727 x = -0.82870727 Simplifying x = -0.82870727Subproblem 2
x + 3.833333334 = -3.004626064 Simplifying x + 3.833333334 = -3.004626064 Reorder the terms: 3.833333334 + x = -3.004626064 Solving 3.833333334 + x = -3.004626064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + x = -3.004626064 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = -3.004626064 + -3.833333334 x = -3.004626064 + -3.833333334 Combine like terms: -3.004626064 + -3.833333334 = -6.837959398 x = -6.837959398 Simplifying x = -6.837959398Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.82870727, -6.837959398}
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