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Simplifying -0.5x2 + -1x + 5.7 = 0 Reorder the terms: 5.7 + -1x + -0.5x2 = 0 Solving 5.7 + -1x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -11.4 + 2x + x2 = 0 Move the constant term to the right: Add '11.4' to each side of the equation. -11.4 + 2x + 11.4 + x2 = 0 + 11.4 Reorder the terms: -11.4 + 11.4 + 2x + x2 = 0 + 11.4 Combine like terms: -11.4 + 11.4 = 0.0 0.0 + 2x + x2 = 0 + 11.4 2x + x2 = 0 + 11.4 Combine like terms: 0 + 11.4 = 11.4 2x + x2 = 11.4 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 = 11.4 + 1 Reorder the terms: 1 + 2x + x2 = 11.4 + 1 Combine like terms: 11.4 + 1 = 12.4 1 + 2x + x2 = 12.4 Factor a perfect square on the left side: (x + 1)(x + 1) = 12.4 Calculate the square root of the right side: 3.521363372 Break this problem into two subproblems by setting (x + 1) equal to 3.521363372 and -3.521363372.Subproblem 1
x + 1 = 3.521363372 Simplifying x + 1 = 3.521363372 Reorder the terms: 1 + x = 3.521363372 Solving 1 + x = 3.521363372 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 = 3.521363372 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.521363372 + -1 x = 3.521363372 + -1 Combine like terms: 3.521363372 + -1 = 2.521363372 x = 2.521363372 Simplifying x = 2.521363372Subproblem 2
x + 1 = -3.521363372 Simplifying x + 1 = -3.521363372 Reorder the terms: 1 + x = -3.521363372 Solving 1 + x = -3.521363372 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 = -3.521363372 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.521363372 + -1 x = -3.521363372 + -1 Combine like terms: -3.521363372 + -1 = -4.521363372 x = -4.521363372 Simplifying x = -4.521363372Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.521363372, -4.521363372}
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