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Simplifying 6x2 + 47x + 63 = 0 Reorder the terms: 63 + 47x + 6x2 = 0 Solving 63 + 47x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 10.5 + 7.833333333x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + 7.833333333x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + 7.833333333x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + 7.833333333x + x2 = 0 + -10.5 7.833333333x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 7.833333333x + x2 = -10.5 The x term is 7.833333333x. Take half its coefficient (3.916666667). Square it (15.34027778) and add it to both sides. Add '15.34027778' to each side of the equation. 7.833333333x + 15.34027778 + x2 = -10.5 + 15.34027778 Reorder the terms: 15.34027778 + 7.833333333x + x2 = -10.5 + 15.34027778 Combine like terms: -10.5 + 15.34027778 = 4.84027778 15.34027778 + 7.833333333x + x2 = 4.84027778 Factor a perfect square on the left side: (x + 3.916666667)(x + 3.916666667) = 4.84027778 Calculate the square root of the right side: 2.200063131 Break this problem into two subproblems by setting (x + 3.916666667) equal to 2.200063131 and -2.200063131.Subproblem 1
x + 3.916666667 = 2.200063131 Simplifying x + 3.916666667 = 2.200063131 Reorder the terms: 3.916666667 + x = 2.200063131 Solving 3.916666667 + x = 2.200063131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.916666667' to each side of the equation. 3.916666667 + -3.916666667 + x = 2.200063131 + -3.916666667 Combine like terms: 3.916666667 + -3.916666667 = 0.000000000 0.000000000 + x = 2.200063131 + -3.916666667 x = 2.200063131 + -3.916666667 Combine like terms: 2.200063131 + -3.916666667 = -1.716603536 x = -1.716603536 Simplifying x = -1.716603536Subproblem 2
x + 3.916666667 = -2.200063131 Simplifying x + 3.916666667 = -2.200063131 Reorder the terms: 3.916666667 + x = -2.200063131 Solving 3.916666667 + x = -2.200063131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.916666667' to each side of the equation. 3.916666667 + -3.916666667 + x = -2.200063131 + -3.916666667 Combine like terms: 3.916666667 + -3.916666667 = 0.000000000 0.000000000 + x = -2.200063131 + -3.916666667 x = -2.200063131 + -3.916666667 Combine like terms: -2.200063131 + -3.916666667 = -6.116729798 x = -6.116729798 Simplifying x = -6.116729798Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.716603536, -6.116729798}
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