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Simplifying 7x2 + -7x + -8 = 0 Reorder the terms: -8 + -7x + 7x2 = 0 Solving -8 + -7x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -1x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -1x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -1x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -1x + x2 = 0 + 1.142857143 -1x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -1x + x2 = 1.142857143 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.142857143 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.142857143 + 0.25 Combine like terms: 1.142857143 + 0.25 = 1.392857143 0.25 + -1x + x2 = 1.392857143 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.392857143 Calculate the square root of the right side: 1.180193689 Break this problem into two subproblems by setting (x + -0.5) equal to 1.180193689 and -1.180193689.Subproblem 1
x + -0.5 = 1.180193689 Simplifying x + -0.5 = 1.180193689 Reorder the terms: -0.5 + x = 1.180193689 Solving -0.5 + x = 1.180193689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.180193689 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.180193689 + 0.5 x = 1.180193689 + 0.5 Combine like terms: 1.180193689 + 0.5 = 1.680193689 x = 1.680193689 Simplifying x = 1.680193689Subproblem 2
x + -0.5 = -1.180193689 Simplifying x + -0.5 = -1.180193689 Reorder the terms: -0.5 + x = -1.180193689 Solving -0.5 + x = -1.180193689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.180193689 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.180193689 + 0.5 x = -1.180193689 + 0.5 Combine like terms: -1.180193689 + 0.5 = -0.680193689 x = -0.680193689 Simplifying x = -0.680193689Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.680193689, -0.680193689}
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