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Simplifying 6x2 + 23x + -378 = 0 Reorder the terms: -378 + 23x + 6x2 = 0 Solving -378 + 23x + 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'. -63 + 3.833333333x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 3.833333333x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 3.833333333x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 3.833333333x + x2 = 0 + 63 3.833333333x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 3.833333333x + x2 = 63 The x term is 3.833333333x. Take half its coefficient (1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. 3.833333333x + 3.673611112 + x2 = 63 + 3.673611112 Reorder the terms: 3.673611112 + 3.833333333x + x2 = 63 + 3.673611112 Combine like terms: 63 + 3.673611112 = 66.673611112 3.673611112 + 3.833333333x + x2 = 66.673611112 Factor a perfect square on the left side: (x + 1.916666667)(x + 1.916666667) = 66.673611112 Calculate the square root of the right side: 8.165391057 Break this problem into two subproblems by setting (x + 1.916666667) equal to 8.165391057 and -8.165391057.Subproblem 1
x + 1.916666667 = 8.165391057 Simplifying x + 1.916666667 = 8.165391057 Reorder the terms: 1.916666667 + x = 8.165391057 Solving 1.916666667 + x = 8.165391057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = 8.165391057 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = 8.165391057 + -1.916666667 x = 8.165391057 + -1.916666667 Combine like terms: 8.165391057 + -1.916666667 = 6.24872439 x = 6.24872439 Simplifying x = 6.24872439Subproblem 2
x + 1.916666667 = -8.165391057 Simplifying x + 1.916666667 = -8.165391057 Reorder the terms: 1.916666667 + x = -8.165391057 Solving 1.916666667 + x = -8.165391057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = -8.165391057 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = -8.165391057 + -1.916666667 x = -8.165391057 + -1.916666667 Combine like terms: -8.165391057 + -1.916666667 = -10.082057724 x = -10.082057724 Simplifying x = -10.082057724Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.24872439, -10.082057724}
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