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Simplifying x * x + -1x = 14.5 Multiply x * x x2 + -1x = 14.5 Reorder the terms: -1x + x2 = 14.5 Solving -1x + x2 = 14.5 Solving for variable 'x'. Reorder the terms: -14.5 + -1x + x2 = 14.5 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 -14.5 + -1x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + -1x + 14.5 + x2 = 0.0 + 14.5 Reorder the terms: -14.5 + 14.5 + -1x + x2 = 0.0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + -1x + x2 = 0.0 + 14.5 -1x + x2 = 0.0 + 14.5 Combine like terms: 0.0 + 14.5 = 14.5 -1x + x2 = 14.5 The x term is -1x. 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 = 14.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 14.5 + 0.25 Combine like terms: 14.5 + 0.25 = 14.75 0.25 + -1x + x2 = 14.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 14.75 Calculate the square root of the right side: 3.840572874 Break this problem into two subproblems by setting (x + -0.5) equal to 3.840572874 and -3.840572874.Subproblem 1
x + -0.5 = 3.840572874 Simplifying x + -0.5 = 3.840572874 Reorder the terms: -0.5 + x = 3.840572874 Solving -0.5 + x = 3.840572874 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 = 3.840572874 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.840572874 + 0.5 x = 3.840572874 + 0.5 Combine like terms: 3.840572874 + 0.5 = 4.340572874 x = 4.340572874 Simplifying x = 4.340572874Subproblem 2
x + -0.5 = -3.840572874 Simplifying x + -0.5 = -3.840572874 Reorder the terms: -0.5 + x = -3.840572874 Solving -0.5 + x = -3.840572874 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 = -3.840572874 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.840572874 + 0.5 x = -3.840572874 + 0.5 Combine like terms: -3.840572874 + 0.5 = -3.340572874 x = -3.340572874 Simplifying x = -3.340572874Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.340572874, -3.340572874}
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