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Simplifying 29 + -6x(3x + -22) = 120 Reorder the terms: 29 + -6x(-22 + 3x) = 120 29 + (-22 * -6x + 3x * -6x) = 120 29 + (132x + -18x2) = 120 Solving 29 + 132x + -18x2 = 120 Solving for variable 'x'. Reorder the terms: 29 + -120 + 132x + -18x2 = 120 + -120 Combine like terms: 29 + -120 = -91 -91 + 132x + -18x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -91 + 132x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. 5.055555556 + -7.333333333x + x2 = 0 Move the constant term to the right: Add '-5.055555556' to each side of the equation. 5.055555556 + -7.333333333x + -5.055555556 + x2 = 0 + -5.055555556 Reorder the terms: 5.055555556 + -5.055555556 + -7.333333333x + x2 = 0 + -5.055555556 Combine like terms: 5.055555556 + -5.055555556 = 0.000000000 0.000000000 + -7.333333333x + x2 = 0 + -5.055555556 -7.333333333x + x2 = 0 + -5.055555556 Combine like terms: 0 + -5.055555556 = -5.055555556 -7.333333333x + x2 = -5.055555556 The x term is -7.333333333x. Take half its coefficient (-3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. -7.333333333x + 13.44444445 + x2 = -5.055555556 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333x + x2 = -5.055555556 + 13.44444445 Combine like terms: -5.055555556 + 13.44444445 = 8.388888894 13.44444445 + -7.333333333x + x2 = 8.388888894 Factor a perfect square on the left side: (x + -3.666666667)(x + -3.666666667) = 8.388888894 Calculate the square root of the right side: 2.896357867 Break this problem into two subproblems by setting (x + -3.666666667) equal to 2.896357867 and -2.896357867.Subproblem 1
x + -3.666666667 = 2.896357867 Simplifying x + -3.666666667 = 2.896357867 Reorder the terms: -3.666666667 + x = 2.896357867 Solving -3.666666667 + x = 2.896357867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + x = 2.896357867 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = 2.896357867 + 3.666666667 x = 2.896357867 + 3.666666667 Combine like terms: 2.896357867 + 3.666666667 = 6.563024534 x = 6.563024534 Simplifying x = 6.563024534Subproblem 2
x + -3.666666667 = -2.896357867 Simplifying x + -3.666666667 = -2.896357867 Reorder the terms: -3.666666667 + x = -2.896357867 Solving -3.666666667 + x = -2.896357867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + x = -2.896357867 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = -2.896357867 + 3.666666667 x = -2.896357867 + 3.666666667 Combine like terms: -2.896357867 + 3.666666667 = 0.7703088 x = 0.7703088 Simplifying x = 0.7703088Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.563024534, 0.7703088}
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