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Simplifying x2 + -30x = 161 Reorder the terms: -30x + x2 = 161 Solving -30x + x2 = 161 Solving for variable 'x'. Reorder the terms: -161 + -30x + x2 = 161 + -161 Combine like terms: 161 + -161 = 0 -161 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '161' to each side of the equation. -161 + -30x + 161 + x2 = 0 + 161 Reorder the terms: -161 + 161 + -30x + x2 = 0 + 161 Combine like terms: -161 + 161 = 0 0 + -30x + x2 = 0 + 161 -30x + x2 = 0 + 161 Combine like terms: 0 + 161 = 161 -30x + x2 = 161 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 161 + 225 Reorder the terms: 225 + -30x + x2 = 161 + 225 Combine like terms: 161 + 225 = 386 225 + -30x + x2 = 386 Factor a perfect square on the left side: (x + -15)(x + -15) = 386 Calculate the square root of the right side: 19.646882704 Break this problem into two subproblems by setting (x + -15) equal to 19.646882704 and -19.646882704.Subproblem 1
x + -15 = 19.646882704 Simplifying x + -15 = 19.646882704 Reorder the terms: -15 + x = 19.646882704 Solving -15 + x = 19.646882704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 19.646882704 + 15 Combine like terms: -15 + 15 = 0 0 + x = 19.646882704 + 15 x = 19.646882704 + 15 Combine like terms: 19.646882704 + 15 = 34.646882704 x = 34.646882704 Simplifying x = 34.646882704Subproblem 2
x + -15 = -19.646882704 Simplifying x + -15 = -19.646882704 Reorder the terms: -15 + x = -19.646882704 Solving -15 + x = -19.646882704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -19.646882704 + 15 Combine like terms: -15 + 15 = 0 0 + x = -19.646882704 + 15 x = -19.646882704 + 15 Combine like terms: -19.646882704 + 15 = -4.646882704 x = -4.646882704 Simplifying x = -4.646882704Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.646882704, -4.646882704}
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