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Simplifying x2 + x + -7 = 234 Reorder the terms: -7 + x + x2 = 234 Solving -7 + x + x2 = 234 Solving for variable 'x'. Reorder the terms: -7 + -234 + x + x2 = 234 + -234 Combine like terms: -7 + -234 = -241 -241 + x + x2 = 234 + -234 Combine like terms: 234 + -234 = 0 -241 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '241' to each side of the equation. -241 + x + 241 + x2 = 0 + 241 Reorder the terms: -241 + 241 + x + x2 = 0 + 241 Combine like terms: -241 + 241 = 0 0 + x + x2 = 0 + 241 x + x2 = 0 + 241 Combine like terms: 0 + 241 = 241 x + x2 = 241 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 = 241 + 0.25 Reorder the terms: 0.25 + x + x2 = 241 + 0.25 Combine like terms: 241 + 0.25 = 241.25 0.25 + x + x2 = 241.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 241.25 Calculate the square root of the right side: 15.532224567 Break this problem into two subproblems by setting (x + 0.5) equal to 15.532224567 and -15.532224567.Subproblem 1
x + 0.5 = 15.532224567 Simplifying x + 0.5 = 15.532224567 Reorder the terms: 0.5 + x = 15.532224567 Solving 0.5 + x = 15.532224567 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 = 15.532224567 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 15.532224567 + -0.5 x = 15.532224567 + -0.5 Combine like terms: 15.532224567 + -0.5 = 15.032224567 x = 15.032224567 Simplifying x = 15.032224567Subproblem 2
x + 0.5 = -15.532224567 Simplifying x + 0.5 = -15.532224567 Reorder the terms: 0.5 + x = -15.532224567 Solving 0.5 + x = -15.532224567 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 = -15.532224567 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -15.532224567 + -0.5 x = -15.532224567 + -0.5 Combine like terms: -15.532224567 + -0.5 = -16.032224567 x = -16.032224567 Simplifying x = -16.032224567Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.032224567, -16.032224567}
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