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Simplifying 3x2 + -69x = 6x2 + -7x + -48 Reorder the terms: -69x + 3x2 = 6x2 + -7x + -48 Reorder the terms: -69x + 3x2 = -48 + -7x + 6x2 Solving -69x + 3x2 = -48 + -7x + 6x2 Solving for variable 'x'. Reorder the terms: 48 + -69x + 7x + 3x2 + -6x2 = -48 + -7x + 6x2 + 48 + 7x + -6x2 Combine like terms: -69x + 7x = -62x 48 + -62x + 3x2 + -6x2 = -48 + -7x + 6x2 + 48 + 7x + -6x2 Combine like terms: 3x2 + -6x2 = -3x2 48 + -62x + -3x2 = -48 + -7x + 6x2 + 48 + 7x + -6x2 Reorder the terms: 48 + -62x + -3x2 = -48 + 48 + -7x + 7x + 6x2 + -6x2 Combine like terms: -48 + 48 = 0 48 + -62x + -3x2 = 0 + -7x + 7x + 6x2 + -6x2 48 + -62x + -3x2 = -7x + 7x + 6x2 + -6x2 Combine like terms: -7x + 7x = 0 48 + -62x + -3x2 = 0 + 6x2 + -6x2 48 + -62x + -3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 48 + -62x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -16 + 20.66666667x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 20.66666667x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 20.66666667x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 20.66666667x + x2 = 0 + 16 20.66666667x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 20.66666667x + x2 = 16 The x term is 20.66666667x. Take half its coefficient (10.33333334). Square it (106.7777779) and add it to both sides. Add '106.7777779' to each side of the equation. 20.66666667x + 106.7777779 + x2 = 16 + 106.7777779 Reorder the terms: 106.7777779 + 20.66666667x + x2 = 16 + 106.7777779 Combine like terms: 16 + 106.7777779 = 122.7777779 106.7777779 + 20.66666667x + x2 = 122.7777779 Factor a perfect square on the left side: (x + 10.33333334)(x + 10.33333334) = 122.7777779 Calculate the square root of the right side: 11.080513431 Break this problem into two subproblems by setting (x + 10.33333334) equal to 11.080513431 and -11.080513431.Subproblem 1
x + 10.33333334 = 11.080513431 Simplifying x + 10.33333334 = 11.080513431 Reorder the terms: 10.33333334 + x = 11.080513431 Solving 10.33333334 + x = 11.080513431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.33333334' to each side of the equation. 10.33333334 + -10.33333334 + x = 11.080513431 + -10.33333334 Combine like terms: 10.33333334 + -10.33333334 = 0.00000000 0.00000000 + x = 11.080513431 + -10.33333334 x = 11.080513431 + -10.33333334 Combine like terms: 11.080513431 + -10.33333334 = 0.747180091 x = 0.747180091 Simplifying x = 0.747180091Subproblem 2
x + 10.33333334 = -11.080513431 Simplifying x + 10.33333334 = -11.080513431 Reorder the terms: 10.33333334 + x = -11.080513431 Solving 10.33333334 + x = -11.080513431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.33333334' to each side of the equation. 10.33333334 + -10.33333334 + x = -11.080513431 + -10.33333334 Combine like terms: 10.33333334 + -10.33333334 = 0.00000000 0.00000000 + x = -11.080513431 + -10.33333334 x = -11.080513431 + -10.33333334 Combine like terms: -11.080513431 + -10.33333334 = -21.413846771 x = -21.413846771 Simplifying x = -21.413846771Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.747180091, -21.413846771}
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