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Simplifying 0.96x2 + -2x + 0.96 = 0 Reorder the terms: 0.96 + -2x + 0.96x2 = 0 Solving 0.96 + -2x + 0.96x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.96 the coefficient of the squared term: Divide each side by '0.96'. 1 + -2.083333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.083333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.083333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.083333333x + x2 = 0 + -1 -2.083333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.083333333x + x2 = -1 The x term is -2.083333333x. Take half its coefficient (-1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. -2.083333333x + 1.085069445 + x2 = -1 + 1.085069445 Reorder the terms: 1.085069445 + -2.083333333x + x2 = -1 + 1.085069445 Combine like terms: -1 + 1.085069445 = 0.085069445 1.085069445 + -2.083333333x + x2 = 0.085069445 Factor a perfect square on the left side: (x + -1.041666667)(x + -1.041666667) = 0.085069445 Calculate the square root of the right side: 0.291666668 Break this problem into two subproblems by setting (x + -1.041666667) equal to 0.291666668 and -0.291666668.Subproblem 1
x + -1.041666667 = 0.291666668 Simplifying x + -1.041666667 = 0.291666668 Reorder the terms: -1.041666667 + x = 0.291666668 Solving -1.041666667 + x = 0.291666668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = 0.291666668 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = 0.291666668 + 1.041666667 x = 0.291666668 + 1.041666667 Combine like terms: 0.291666668 + 1.041666667 = 1.333333335 x = 1.333333335 Simplifying x = 1.333333335Subproblem 2
x + -1.041666667 = -0.291666668 Simplifying x + -1.041666667 = -0.291666668 Reorder the terms: -1.041666667 + x = -0.291666668 Solving -1.041666667 + x = -0.291666668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = -0.291666668 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = -0.291666668 + 1.041666667 x = -0.291666668 + 1.041666667 Combine like terms: -0.291666668 + 1.041666667 = 0.749999999 x = 0.749999999 Simplifying x = 0.749999999Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.333333335, 0.749999999}
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