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Simplifying 7x + -8 = 7x2 + -49x Reorder the terms: -8 + 7x = 7x2 + -49x Reorder the terms: -8 + 7x = -49x + 7x2 Solving -8 + 7x = -49x + 7x2 Solving for variable 'x'. Combine like terms: 7x + 49x = 56x -8 + 56x + -7x2 = -49x + 7x2 + 49x + -7x2 Reorder the terms: -8 + 56x + -7x2 = -49x + 49x + 7x2 + -7x2 Combine like terms: -49x + 49x = 0 -8 + 56x + -7x2 = 0 + 7x2 + -7x2 -8 + 56x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -8 + 56x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 1.142857143 + -8x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + -8x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + -8x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + -8x + x2 = 0 + -1.142857143 -8x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 -8x + x2 = -1.142857143 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -1.142857143 + 16 Reorder the terms: 16 + -8x + x2 = -1.142857143 + 16 Combine like terms: -1.142857143 + 16 = 14.857142857 16 + -8x + x2 = 14.857142857 Factor a perfect square on the left side: (x + -4)(x + -4) = 14.857142857 Calculate the square root of the right side: 3.854496447 Break this problem into two subproblems by setting (x + -4) equal to 3.854496447 and -3.854496447.Subproblem 1
x + -4 = 3.854496447 Simplifying x + -4 = 3.854496447 Reorder the terms: -4 + x = 3.854496447 Solving -4 + x = 3.854496447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.854496447 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.854496447 + 4 x = 3.854496447 + 4 Combine like terms: 3.854496447 + 4 = 7.854496447 x = 7.854496447 Simplifying x = 7.854496447Subproblem 2
x + -4 = -3.854496447 Simplifying x + -4 = -3.854496447 Reorder the terms: -4 + x = -3.854496447 Solving -4 + x = -3.854496447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.854496447 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.854496447 + 4 x = -3.854496447 + 4 Combine like terms: -3.854496447 + 4 = 0.145503553 x = 0.145503553 Simplifying x = 0.145503553Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.854496447, 0.145503553}
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