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Simplifying x2 + -2x + -0.9375 = 0 Reorder the terms: -0.9375 + -2x + x2 = 0 Solving -0.9375 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -2x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -2x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -2x + x2 = 0 + 0.9375 -2x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -2x + x2 = 0.9375 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.9375 + 1 Reorder the terms: 1 + -2x + x2 = 0.9375 + 1 Combine like terms: 0.9375 + 1 = 1.9375 1 + -2x + x2 = 1.9375 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.9375 Calculate the square root of the right side: 1.391941091 Break this problem into two subproblems by setting (x + -1) equal to 1.391941091 and -1.391941091.Subproblem 1
x + -1 = 1.391941091 Simplifying x + -1 = 1.391941091 Reorder the terms: -1 + x = 1.391941091 Solving -1 + x = 1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.391941091 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.391941091 + 1 x = 1.391941091 + 1 Combine like terms: 1.391941091 + 1 = 2.391941091 x = 2.391941091 Simplifying x = 2.391941091Subproblem 2
x + -1 = -1.391941091 Simplifying x + -1 = -1.391941091 Reorder the terms: -1 + x = -1.391941091 Solving -1 + x = -1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.391941091 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.391941091 + 1 x = -1.391941091 + 1 Combine like terms: -1.391941091 + 1 = -0.391941091 x = -0.391941091 Simplifying x = -0.391941091Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.391941091, -0.391941091}
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