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Simplifying 0 = -39x2 + -12x + 95 Reorder the terms: 0 = 95 + -12x + -39x2 Solving 0 = 95 + -12x + -39x2 Solving for variable 'x'. Combine like terms: 0 + -95 = -95 -95 + 12x + 39x2 = 95 + -12x + -39x2 + -95 + 12x + 39x2 Reorder the terms: -95 + 12x + 39x2 = 95 + -95 + -12x + 12x + -39x2 + 39x2 Combine like terms: 95 + -95 = 0 -95 + 12x + 39x2 = 0 + -12x + 12x + -39x2 + 39x2 -95 + 12x + 39x2 = -12x + 12x + -39x2 + 39x2 Combine like terms: -12x + 12x = 0 -95 + 12x + 39x2 = 0 + -39x2 + 39x2 -95 + 12x + 39x2 = -39x2 + 39x2 Combine like terms: -39x2 + 39x2 = 0 -95 + 12x + 39x2 = 0 Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. -2.435897436 + 0.3076923077x + x2 = 0 Move the constant term to the right: Add '2.435897436' to each side of the equation. -2.435897436 + 0.3076923077x + 2.435897436 + x2 = 0 + 2.435897436 Reorder the terms: -2.435897436 + 2.435897436 + 0.3076923077x + x2 = 0 + 2.435897436 Combine like terms: -2.435897436 + 2.435897436 = 0.000000000 0.000000000 + 0.3076923077x + x2 = 0 + 2.435897436 0.3076923077x + x2 = 0 + 2.435897436 Combine like terms: 0 + 2.435897436 = 2.435897436 0.3076923077x + x2 = 2.435897436 The x term is 0.3076923077x. Take half its coefficient (0.1538461539). Square it (0.02366863907) and add it to both sides. Add '0.02366863907' to each side of the equation. 0.3076923077x + 0.02366863907 + x2 = 2.435897436 + 0.02366863907 Reorder the terms: 0.02366863907 + 0.3076923077x + x2 = 2.435897436 + 0.02366863907 Combine like terms: 2.435897436 + 0.02366863907 = 2.45956607507 0.02366863907 + 0.3076923077x + x2 = 2.45956607507 Factor a perfect square on the left side: (x + 0.1538461539)(x + 0.1538461539) = 2.45956607507 Calculate the square root of the right side: 1.568300378 Break this problem into two subproblems by setting (x + 0.1538461539) equal to 1.568300378 and -1.568300378.Subproblem 1
x + 0.1538461539 = 1.568300378 Simplifying x + 0.1538461539 = 1.568300378 Reorder the terms: 0.1538461539 + x = 1.568300378 Solving 0.1538461539 + x = 1.568300378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1538461539' to each side of the equation. 0.1538461539 + -0.1538461539 + x = 1.568300378 + -0.1538461539 Combine like terms: 0.1538461539 + -0.1538461539 = 0.0000000000 0.0000000000 + x = 1.568300378 + -0.1538461539 x = 1.568300378 + -0.1538461539 Combine like terms: 1.568300378 + -0.1538461539 = 1.4144542241 x = 1.4144542241 Simplifying x = 1.4144542241Subproblem 2
x + 0.1538461539 = -1.568300378 Simplifying x + 0.1538461539 = -1.568300378 Reorder the terms: 0.1538461539 + x = -1.568300378 Solving 0.1538461539 + x = -1.568300378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1538461539' to each side of the equation. 0.1538461539 + -0.1538461539 + x = -1.568300378 + -0.1538461539 Combine like terms: 0.1538461539 + -0.1538461539 = 0.0000000000 0.0000000000 + x = -1.568300378 + -0.1538461539 x = -1.568300378 + -0.1538461539 Combine like terms: -1.568300378 + -0.1538461539 = -1.7221465319 x = -1.7221465319 Simplifying x = -1.7221465319Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4144542241, -1.7221465319}
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