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Simplifying x + 12(x)(x) + -5 = 31 Multiply x * x x + 12x2 + -5 = 31 Reorder the terms: -5 + x + 12x2 = 31 Solving -5 + x + 12x2 = 31 Solving for variable 'x'. Reorder the terms: -5 + -31 + x + 12x2 = 31 + -31 Combine like terms: -5 + -31 = -36 -36 + x + 12x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -36 + x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3 + 0.08333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.08333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.08333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.08333333333x + x2 = 0 + 3 0.08333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.08333333333x + x2 = 3 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. 0.08333333333x + 0.25 + x2 = 3 + 0.25 Reorder the terms: 0.25 + 0.08333333333x + x2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + 0.08333333333x + x2 = 3.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 0.5 = 1.802775638 Simplifying x + 0.5 = 1.802775638 Reorder the terms: 0.5 + x = 1.802775638 Solving 0.5 + x = 1.802775638 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 = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.802775638 + -0.5 x = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 x = 1.302775638 Simplifying x = 1.302775638Subproblem 2
x + 0.5 = -1.802775638 Simplifying x + 0.5 = -1.802775638 Reorder the terms: 0.5 + x = -1.802775638 Solving 0.5 + x = -1.802775638 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 = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.802775638 + -0.5 x = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 x = -2.302775638 Simplifying x = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.302775638, -2.302775638}
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