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Simplifying x2 + x = 143 Reorder the terms: x + x2 = 143 Solving x + x2 = 143 Solving for variable 'x'. Reorder the terms: -143 + x + x2 = 143 + -143 Combine like terms: 143 + -143 = 0 -143 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '143' to each side of the equation. -143 + x + 143 + x2 = 0 + 143 Reorder the terms: -143 + 143 + x + x2 = 0 + 143 Combine like terms: -143 + 143 = 0 0 + x + x2 = 0 + 143 x + x2 = 0 + 143 Combine like terms: 0 + 143 = 143 x + x2 = 143 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 = 143 + 0.25 Reorder the terms: 0.25 + x + x2 = 143 + 0.25 Combine like terms: 143 + 0.25 = 143.25 0.25 + x + x2 = 143.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 143.25 Calculate the square root of the right side: 11.968709204 Break this problem into two subproblems by setting (x + 0.5) equal to 11.968709204 and -11.968709204.Subproblem 1
x + 0.5 = 11.968709204 Simplifying x + 0.5 = 11.968709204 Reorder the terms: 0.5 + x = 11.968709204 Solving 0.5 + x = 11.968709204 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 = 11.968709204 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.968709204 + -0.5 x = 11.968709204 + -0.5 Combine like terms: 11.968709204 + -0.5 = 11.468709204 x = 11.468709204 Simplifying x = 11.468709204Subproblem 2
x + 0.5 = -11.968709204 Simplifying x + 0.5 = -11.968709204 Reorder the terms: 0.5 + x = -11.968709204 Solving 0.5 + x = -11.968709204 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 = -11.968709204 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.968709204 + -0.5 x = -11.968709204 + -0.5 Combine like terms: -11.968709204 + -0.5 = -12.468709204 x = -12.468709204 Simplifying x = -12.468709204Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.468709204, -12.468709204}
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