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Simplifying 0 = x2 + -0.175 + -1x Reorder the terms: 0 = -0.175 + -1x + x2 Solving 0 = -0.175 + -1x + x2 Solving for variable 'x'. Combine like terms: 0 + 0.175 = 0.175 0.175 + x + -1x2 = -0.175 + -1x + x2 + 0.175 + x + -1x2 Reorder the terms: 0.175 + x + -1x2 = -0.175 + 0.175 + -1x + x + x2 + -1x2 Combine like terms: -0.175 + 0.175 = 0.000 0.175 + x + -1x2 = 0.000 + -1x + x + x2 + -1x2 0.175 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 0.175 + x + -1x2 = 0 + x2 + -1x2 0.175 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.175 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.175 + -1x + x2 = 0 Move the constant term to the right: Add '0.175' to each side of the equation. -0.175 + -1x + 0.175 + x2 = 0 + 0.175 Reorder the terms: -0.175 + 0.175 + -1x + x2 = 0 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + -1x + x2 = 0 + 0.175 -1x + x2 = 0 + 0.175 Combine like terms: 0 + 0.175 = 0.175 -1x + x2 = 0.175 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. -1x + 0.25 + x2 = 0.175 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.175 + 0.25 Combine like terms: 0.175 + 0.25 = 0.425 0.25 + -1x + x2 = 0.425 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.425 Calculate the square root of the right side: 0.651920241 Break this problem into two subproblems by setting (x + 0.5) equal to 0.651920241 and -0.651920241.Subproblem 1
x + 0.5 = 0.651920241 Simplifying x + 0.5 = 0.651920241 Reorder the terms: 0.5 + x = 0.651920241 Solving 0.5 + x = 0.651920241 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 = 0.651920241 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.651920241 + -0.5 x = 0.651920241 + -0.5 Combine like terms: 0.651920241 + -0.5 = 0.151920241 x = 0.151920241 Simplifying x = 0.151920241Subproblem 2
x + 0.5 = -0.651920241 Simplifying x + 0.5 = -0.651920241 Reorder the terms: 0.5 + x = -0.651920241 Solving 0.5 + x = -0.651920241 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 = -0.651920241 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.651920241 + -0.5 x = -0.651920241 + -0.5 Combine like terms: -0.651920241 + -0.5 = -1.151920241 x = -1.151920241 Simplifying x = -1.151920241Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.151920241, -1.151920241}
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