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Simplifying 8x2 + -10x + -20 = 5x2 + 1 Reorder the terms: -20 + -10x + 8x2 = 5x2 + 1 Reorder the terms: -20 + -10x + 8x2 = 1 + 5x2 Solving -20 + -10x + 8x2 = 1 + 5x2 Solving for variable 'x'. Reorder the terms: -20 + -1 + -10x + 8x2 + -5x2 = 1 + 5x2 + -1 + -5x2 Combine like terms: -20 + -1 = -21 -21 + -10x + 8x2 + -5x2 = 1 + 5x2 + -1 + -5x2 Combine like terms: 8x2 + -5x2 = 3x2 -21 + -10x + 3x2 = 1 + 5x2 + -1 + -5x2 Reorder the terms: -21 + -10x + 3x2 = 1 + -1 + 5x2 + -5x2 Combine like terms: 1 + -1 = 0 -21 + -10x + 3x2 = 0 + 5x2 + -5x2 -21 + -10x + 3x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -21 + -10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -3.333333333x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -3.333333333x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3.333333333x + x2 = 0 + 7 -3.333333333x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -3.333333333x + x2 = 7 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 7 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 7 + 2.777777779 Combine like terms: 7 + 2.777777779 = 9.777777779 2.777777779 + -3.333333333x + x2 = 9.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 9.777777779 Calculate the square root of the right side: 3.12694384 Break this problem into two subproblems by setting (x + -1.666666667) equal to 3.12694384 and -3.12694384.Subproblem 1
x + -1.666666667 = 3.12694384 Simplifying x + -1.666666667 = 3.12694384 Reorder the terms: -1.666666667 + x = 3.12694384 Solving -1.666666667 + x = 3.12694384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 3.12694384 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 3.12694384 + 1.666666667 x = 3.12694384 + 1.666666667 Combine like terms: 3.12694384 + 1.666666667 = 4.793610507 x = 4.793610507 Simplifying x = 4.793610507Subproblem 2
x + -1.666666667 = -3.12694384 Simplifying x + -1.666666667 = -3.12694384 Reorder the terms: -1.666666667 + x = -3.12694384 Solving -1.666666667 + x = -3.12694384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -3.12694384 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -3.12694384 + 1.666666667 x = -3.12694384 + 1.666666667 Combine like terms: -3.12694384 + 1.666666667 = -1.460277173 x = -1.460277173 Simplifying x = -1.460277173Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.793610507, -1.460277173}
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