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Simplifying 10x2 + -10x + -9 = 0 Reorder the terms: -9 + -10x + 10x2 = 0 Solving -9 + -10x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + -1x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + -1x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + -1x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + -1x + x2 = 0 + 0.9 -1x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 -1x + x2 = 0.9 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 = 0.9 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.9 + 0.25 Combine like terms: 0.9 + 0.25 = 1.15 0.25 + -1x + x2 = 1.15 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.15 Calculate the square root of the right side: 1.072380529 Break this problem into two subproblems by setting (x + -0.5) equal to 1.072380529 and -1.072380529.Subproblem 1
x + -0.5 = 1.072380529 Simplifying x + -0.5 = 1.072380529 Reorder the terms: -0.5 + x = 1.072380529 Solving -0.5 + x = 1.072380529 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 = 1.072380529 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.072380529 + 0.5 x = 1.072380529 + 0.5 Combine like terms: 1.072380529 + 0.5 = 1.572380529 x = 1.572380529 Simplifying x = 1.572380529Subproblem 2
x + -0.5 = -1.072380529 Simplifying x + -0.5 = -1.072380529 Reorder the terms: -0.5 + x = -1.072380529 Solving -0.5 + x = -1.072380529 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 = -1.072380529 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.072380529 + 0.5 x = -1.072380529 + 0.5 Combine like terms: -1.072380529 + 0.5 = -0.572380529 x = -0.572380529 Simplifying x = -0.572380529Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.572380529, -0.572380529}
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