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Simplifying x + 3 + x2 + 4 = 90 Reorder the terms: 3 + 4 + x + x2 = 90 Combine like terms: 3 + 4 = 7 7 + x + x2 = 90 Solving 7 + x + x2 = 90 Solving for variable 'x'. Reorder the terms: 7 + -90 + x + x2 = 90 + -90 Combine like terms: 7 + -90 = -83 -83 + x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -83 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '83' to each side of the equation. -83 + x + 83 + x2 = 0 + 83 Reorder the terms: -83 + 83 + x + x2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + x + x2 = 0 + 83 x + x2 = 0 + 83 Combine like terms: 0 + 83 = 83 x + x2 = 83 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 = 83 + 0.25 Reorder the terms: 0.25 + x + x2 = 83 + 0.25 Combine like terms: 83 + 0.25 = 83.25 0.25 + x + x2 = 83.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 83.25 Calculate the square root of the right side: 9.124143795 Break this problem into two subproblems by setting (x + 0.5) equal to 9.124143795 and -9.124143795.Subproblem 1
x + 0.5 = 9.124143795 Simplifying x + 0.5 = 9.124143795 Reorder the terms: 0.5 + x = 9.124143795 Solving 0.5 + x = 9.124143795 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 = 9.124143795 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.124143795 + -0.5 x = 9.124143795 + -0.5 Combine like terms: 9.124143795 + -0.5 = 8.624143795 x = 8.624143795 Simplifying x = 8.624143795Subproblem 2
x + 0.5 = -9.124143795 Simplifying x + 0.5 = -9.124143795 Reorder the terms: 0.5 + x = -9.124143795 Solving 0.5 + x = -9.124143795 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 = -9.124143795 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.124143795 + -0.5 x = -9.124143795 + -0.5 Combine like terms: -9.124143795 + -0.5 = -9.624143795 x = -9.624143795 Simplifying x = -9.624143795Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.624143795, -9.624143795}
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