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Simplifying 3.998 = x2 + -3x Reorder the terms: 3.998 = -3x + x2 Solving 3.998 = -3x + x2 Solving for variable 'x'. Reorder the terms: 3.998 + 3x + -1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 3.998 + 3x + -1x2 = 0 + x2 + -1x2 3.998 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3.998 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3.998 + -3x + x2 = 0 Move the constant term to the right: Add '3.998' to each side of the equation. -3.998 + -3x + 3.998 + x2 = 0 + 3.998 Reorder the terms: -3.998 + 3.998 + -3x + x2 = 0 + 3.998 Combine like terms: -3.998 + 3.998 = 0.000 0.000 + -3x + x2 = 0 + 3.998 -3x + x2 = 0 + 3.998 Combine like terms: 0 + 3.998 = 3.998 -3x + x2 = 3.998 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 3.998 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 3.998 + 2.25 Combine like terms: 3.998 + 2.25 = 6.248 2.25 + -3x + x2 = 6.248 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 6.248 Calculate the square root of the right side: 2.499599968 Break this problem into two subproblems by setting (x + -1.5) equal to 2.499599968 and -2.499599968.Subproblem 1
x + -1.5 = 2.499599968 Simplifying x + -1.5 = 2.499599968 Reorder the terms: -1.5 + x = 2.499599968 Solving -1.5 + x = 2.499599968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.499599968 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.499599968 + 1.5 x = 2.499599968 + 1.5 Combine like terms: 2.499599968 + 1.5 = 3.999599968 x = 3.999599968 Simplifying x = 3.999599968Subproblem 2
x + -1.5 = -2.499599968 Simplifying x + -1.5 = -2.499599968 Reorder the terms: -1.5 + x = -2.499599968 Solving -1.5 + x = -2.499599968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.499599968 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.499599968 + 1.5 x = -2.499599968 + 1.5 Combine like terms: -2.499599968 + 1.5 = -0.999599968 x = -0.999599968 Simplifying x = -0.999599968Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.999599968, -0.999599968}
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