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Simplifying x2 + x + -2.4 = 150.8 Reorder the terms: -2.4 + x + x2 = 150.8 Solving -2.4 + x + x2 = 150.8 Solving for variable 'x'. Reorder the terms: -2.4 + -150.8 + x + x2 = 150.8 + -150.8 Combine like terms: -2.4 + -150.8 = -153.2 -153.2 + x + x2 = 150.8 + -150.8 Combine like terms: 150.8 + -150.8 = 0.0 -153.2 + x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '153.2' to each side of the equation. -153.2 + x + 153.2 + x2 = 0.0 + 153.2 Reorder the terms: -153.2 + 153.2 + x + x2 = 0.0 + 153.2 Combine like terms: -153.2 + 153.2 = 0.0 0.0 + x + x2 = 0.0 + 153.2 x + x2 = 0.0 + 153.2 Combine like terms: 0.0 + 153.2 = 153.2 x + x2 = 153.2 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. x + 0.25 + x2 = 153.2 + 0.25 Reorder the terms: 0.25 + x + x2 = 153.2 + 0.25 Combine like terms: 153.2 + 0.25 = 153.45 0.25 + x + x2 = 153.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 153.45 Calculate the square root of the right side: 12.387493693 Break this problem into two subproblems by setting (x + 0.5) equal to 12.387493693 and -12.387493693.Subproblem 1
x + 0.5 = 12.387493693 Simplifying x + 0.5 = 12.387493693 Reorder the terms: 0.5 + x = 12.387493693 Solving 0.5 + x = 12.387493693 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 = 12.387493693 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.387493693 + -0.5 x = 12.387493693 + -0.5 Combine like terms: 12.387493693 + -0.5 = 11.887493693 x = 11.887493693 Simplifying x = 11.887493693Subproblem 2
x + 0.5 = -12.387493693 Simplifying x + 0.5 = -12.387493693 Reorder the terms: 0.5 + x = -12.387493693 Solving 0.5 + x = -12.387493693 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 = -12.387493693 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.387493693 + -0.5 x = -12.387493693 + -0.5 Combine like terms: -12.387493693 + -0.5 = -12.887493693 x = -12.887493693 Simplifying x = -12.887493693Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.887493693, -12.887493693}
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