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Simplifying 0 = x2 + -1x + -0.24 Reorder the terms: 0 = -0.24 + -1x + x2 Solving 0 = -0.24 + -1x + x2 Solving for variable 'x'. Combine like terms: 0 + 0.24 = 0.24 0.24 + x + -1x2 = -0.24 + -1x + x2 + 0.24 + x + -1x2 Reorder the terms: 0.24 + x + -1x2 = -0.24 + 0.24 + -1x + x + x2 + -1x2 Combine like terms: -0.24 + 0.24 = 0.00 0.24 + x + -1x2 = 0.00 + -1x + x + x2 + -1x2 0.24 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 0.24 + x + -1x2 = 0 + x2 + -1x2 0.24 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.24 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.24 + -1x + x2 = 0 Move the constant term to the right: Add '0.24' to each side of the equation. -0.24 + -1x + 0.24 + x2 = 0 + 0.24 Reorder the terms: -0.24 + 0.24 + -1x + x2 = 0 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + -1x + x2 = 0 + 0.24 -1x + x2 = 0 + 0.24 Combine like terms: 0 + 0.24 = 0.24 -1x + x2 = 0.24 The x term is x. 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 = 0.24 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.24 + 0.25 Combine like terms: 0.24 + 0.25 = 0.49 0.25 + -1x + x2 = 0.49 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.49 Calculate the square root of the right side: 0.7 Break this problem into two subproblems by setting (x + 0.5) equal to 0.7 and -0.7.Subproblem 1
x + 0.5 = 0.7 Simplifying x + 0.5 = 0.7 Reorder the terms: 0.5 + x = 0.7 Solving 0.5 + x = 0.7 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 = 0.7 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.7 + -0.5 x = 0.7 + -0.5 Combine like terms: 0.7 + -0.5 = 0.2 x = 0.2 Simplifying x = 0.2Subproblem 2
x + 0.5 = -0.7 Simplifying x + 0.5 = -0.7 Reorder the terms: 0.5 + x = -0.7 Solving 0.5 + x = -0.7 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 = -0.7 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.7 + -0.5 x = -0.7 + -0.5 Combine like terms: -0.7 + -0.5 = -1.2 x = -1.2 Simplifying x = -1.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2, -1.2}
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