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Simplifying 0 = x2 + x + -4.6 Reorder the terms: 0 = -4.6 + x + x2 Solving 0 = -4.6 + x + x2 Solving for variable 'x'. Combine like terms: 0 + 4.6 = 4.6 4.6 + -1x + -1x2 = -4.6 + x + x2 + 4.6 + -1x + -1x2 Reorder the terms: 4.6 + -1x + -1x2 = -4.6 + 4.6 + x + -1x + x2 + -1x2 Combine like terms: -4.6 + 4.6 = 0.0 4.6 + -1x + -1x2 = 0.0 + x + -1x + x2 + -1x2 4.6 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 4.6 + -1x + -1x2 = 0 + x2 + -1x2 4.6 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4.6 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4.6 + x + x2 = 0 Move the constant term to the right: Add '4.6' to each side of the equation. -4.6 + x + 4.6 + x2 = 0 + 4.6 Reorder the terms: -4.6 + 4.6 + x + x2 = 0 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + x + x2 = 0 + 4.6 x + x2 = 0 + 4.6 Combine like terms: 0 + 4.6 = 4.6 x + x2 = 4.6 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. + 0.25 + x2 = 4.6 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 4.6 + 0.25 Combine like terms: 4.6 + 0.25 = 4.85 1.25 + x2 = 4.85 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.85 Calculate the square root of the right side: 2.202271555 Break this problem into two subproblems by setting (x + 0.5) equal to 2.202271555 and -2.202271555.Subproblem 1
x + 0.5 = 2.202271555 Simplifying x + 0.5 = 2.202271555 Reorder the terms: 0.5 + x = 2.202271555 Solving 0.5 + x = 2.202271555 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 = 2.202271555 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.202271555 + -0.5 x = 2.202271555 + -0.5 Combine like terms: 2.202271555 + -0.5 = 1.702271555 x = 1.702271555 Simplifying x = 1.702271555Subproblem 2
x + 0.5 = -2.202271555 Simplifying x + 0.5 = -2.202271555 Reorder the terms: 0.5 + x = -2.202271555 Solving 0.5 + x = -2.202271555 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 = -2.202271555 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.202271555 + -0.5 x = -2.202271555 + -0.5 Combine like terms: -2.202271555 + -0.5 = -2.702271555 x = -2.702271555 Simplifying x = -2.702271555Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.702271555, -2.702271555}
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