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Simplifying x2 + 13x + 18x = -3 Reorder the terms: 13x + 18x + x2 = -3 Combine like terms: 13x + 18x = 31x 31x + x2 = -3 Solving 31x + x2 = -3 Solving for variable 'x'. Reorder the terms: 3 + 31x + x2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 31x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 31x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 31x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 31x + x2 = 0 + -3 31x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 31x + x2 = -3 The x term is 31x. Take half its coefficient (15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. 31x + 240.25 + x2 = -3 + 240.25 Reorder the terms: 240.25 + 31x + x2 = -3 + 240.25 Combine like terms: -3 + 240.25 = 237.25 240.25 + 31x + x2 = 237.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 237.25 Calculate the square root of the right side: 15.402921801 Break this problem into two subproblems by setting (x + 15.5) equal to 15.402921801 and -15.402921801.Subproblem 1
x + 15.5 = 15.402921801 Simplifying x + 15.5 = 15.402921801 Reorder the terms: 15.5 + x = 15.402921801 Solving 15.5 + x = 15.402921801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 15.402921801 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 15.402921801 + -15.5 x = 15.402921801 + -15.5 Combine like terms: 15.402921801 + -15.5 = -0.097078199 x = -0.097078199 Simplifying x = -0.097078199Subproblem 2
x + 15.5 = -15.402921801 Simplifying x + 15.5 = -15.402921801 Reorder the terms: 15.5 + x = -15.402921801 Solving 15.5 + x = -15.402921801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -15.402921801 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -15.402921801 + -15.5 x = -15.402921801 + -15.5 Combine like terms: -15.402921801 + -15.5 = -30.902921801 x = -30.902921801 Simplifying x = -30.902921801Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.097078199, -30.902921801}
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