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Simplifying x2 + 3x + -167 = 0 Reorder the terms: -167 + 3x + x2 = 0 Solving -167 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '167' to each side of the equation. -167 + 3x + 167 + x2 = 0 + 167 Reorder the terms: -167 + 167 + 3x + x2 = 0 + 167 Combine like terms: -167 + 167 = 0 0 + 3x + x2 = 0 + 167 3x + x2 = 0 + 167 Combine like terms: 0 + 167 = 167 3x + x2 = 167 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 = 167 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 167 + 2.25 Combine like terms: 167 + 2.25 = 169.25 2.25 + 3x + x2 = 169.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 169.25 Calculate the square root of the right side: 13.009611831 Break this problem into two subproblems by setting (x + 1.5) equal to 13.009611831 and -13.009611831.Subproblem 1
x + 1.5 = 13.009611831 Simplifying x + 1.5 = 13.009611831 Reorder the terms: 1.5 + x = 13.009611831 Solving 1.5 + x = 13.009611831 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 = 13.009611831 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.009611831 + -1.5 x = 13.009611831 + -1.5 Combine like terms: 13.009611831 + -1.5 = 11.509611831 x = 11.509611831 Simplifying x = 11.509611831Subproblem 2
x + 1.5 = -13.009611831 Simplifying x + 1.5 = -13.009611831 Reorder the terms: 1.5 + x = -13.009611831 Solving 1.5 + x = -13.009611831 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 = -13.009611831 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.009611831 + -1.5 x = -13.009611831 + -1.5 Combine like terms: -13.009611831 + -1.5 = -14.509611831 x = -14.509611831 Simplifying x = -14.509611831Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.509611831, -14.509611831}
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