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Simplifying 1.38 = -0.5x2 + x + 4 Reorder the terms: 1.38 = 4 + x + -0.5x2 Solving 1.38 = 4 + x + -0.5x2 Solving for variable 'x'. Combine like terms: 1.38 + -4 = -2.62 -2.62 + -1x + 0.5x2 = 4 + x + -0.5x2 + -4 + -1x + 0.5x2 Reorder the terms: -2.62 + -1x + 0.5x2 = 4 + -4 + x + -1x + -0.5x2 + 0.5x2 Combine like terms: 4 + -4 = 0 -2.62 + -1x + 0.5x2 = 0 + x + -1x + -0.5x2 + 0.5x2 -2.62 + -1x + 0.5x2 = x + -1x + -0.5x2 + 0.5x2 Combine like terms: x + -1x = 0 -2.62 + -1x + 0.5x2 = 0 + -0.5x2 + 0.5x2 -2.62 + -1x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -2.62 + -1x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -5.24 + -2x + x2 = 0 Move the constant term to the right: Add '5.24' to each side of the equation. -5.24 + -2x + 5.24 + x2 = 0 + 5.24 Reorder the terms: -5.24 + 5.24 + -2x + x2 = 0 + 5.24 Combine like terms: -5.24 + 5.24 = 0.00 0.00 + -2x + x2 = 0 + 5.24 -2x + x2 = 0 + 5.24 Combine like terms: 0 + 5.24 = 5.24 -2x + x2 = 5.24 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 = 5.24 + 1 Reorder the terms: 1 + -2x + x2 = 5.24 + 1 Combine like terms: 5.24 + 1 = 6.24 1 + -2x + x2 = 6.24 Factor a perfect square on the left side: (x + -1)(x + -1) = 6.24 Calculate the square root of the right side: 2.497999199 Break this problem into two subproblems by setting (x + -1) equal to 2.497999199 and -2.497999199.Subproblem 1
x + -1 = 2.497999199 Simplifying x + -1 = 2.497999199 Reorder the terms: -1 + x = 2.497999199 Solving -1 + x = 2.497999199 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 = 2.497999199 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.497999199 + 1 x = 2.497999199 + 1 Combine like terms: 2.497999199 + 1 = 3.497999199 x = 3.497999199 Simplifying x = 3.497999199Subproblem 2
x + -1 = -2.497999199 Simplifying x + -1 = -2.497999199 Reorder the terms: -1 + x = -2.497999199 Solving -1 + x = -2.497999199 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 = -2.497999199 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.497999199 + 1 x = -2.497999199 + 1 Combine like terms: -2.497999199 + 1 = -1.497999199 x = -1.497999199 Simplifying x = -1.497999199Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.497999199, -1.497999199}
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