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Simplifying x2 + 3x + -10.01 = 0 Reorder the terms: -10.01 + 3x + x2 = 0 Solving -10.01 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10.01' to each side of the equation. -10.01 + 3x + 10.01 + x2 = 0 + 10.01 Reorder the terms: -10.01 + 10.01 + 3x + x2 = 0 + 10.01 Combine like terms: -10.01 + 10.01 = 0.00 0.00 + 3x + x2 = 0 + 10.01 3x + x2 = 0 + 10.01 Combine like terms: 0 + 10.01 = 10.01 3x + x2 = 10.01 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 10.01 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 10.01 + 2.25 Combine like terms: 10.01 + 2.25 = 12.26 2.25 + 3x + x2 = 12.26 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 12.26 Calculate the square root of the right side: 3.50142828 Break this problem into two subproblems by setting (x + 1.5) equal to 3.50142828 and -3.50142828.Subproblem 1
x + 1.5 = 3.50142828 Simplifying x + 1.5 = 3.50142828 Reorder the terms: 1.5 + x = 3.50142828 Solving 1.5 + x = 3.50142828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.50142828 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.50142828 + -1.5 x = 3.50142828 + -1.5 Combine like terms: 3.50142828 + -1.5 = 2.00142828 x = 2.00142828 Simplifying x = 2.00142828Subproblem 2
x + 1.5 = -3.50142828 Simplifying x + 1.5 = -3.50142828 Reorder the terms: 1.5 + x = -3.50142828 Solving 1.5 + x = -3.50142828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.50142828 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.50142828 + -1.5 x = -3.50142828 + -1.5 Combine like terms: -3.50142828 + -1.5 = -5.00142828 x = -5.00142828 Simplifying x = -5.00142828Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.00142828, -5.00142828}
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