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Simplifying x2 + -30x + -5 = 0 Reorder the terms: -5 + -30x + x2 = 0 Solving -5 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -30x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -30x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -30x + x2 = 0 + 5 -30x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -30x + x2 = 5 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 = 5 + 225 Reorder the terms: 225 + -30x + x2 = 5 + 225 Combine like terms: 5 + 225 = 230 225 + -30x + x2 = 230 Factor a perfect square on the left side: (x + -15)(x + -15) = 230 Calculate the square root of the right side: 15.165750888 Break this problem into two subproblems by setting (x + -15) equal to 15.165750888 and -15.165750888.Subproblem 1
x + -15 = 15.165750888 Simplifying x + -15 = 15.165750888 Reorder the terms: -15 + x = 15.165750888 Solving -15 + x = 15.165750888 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 = 15.165750888 + 15 Combine like terms: -15 + 15 = 0 0 + x = 15.165750888 + 15 x = 15.165750888 + 15 Combine like terms: 15.165750888 + 15 = 30.165750888 x = 30.165750888 Simplifying x = 30.165750888Subproblem 2
x + -15 = -15.165750888 Simplifying x + -15 = -15.165750888 Reorder the terms: -15 + x = -15.165750888 Solving -15 + x = -15.165750888 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 = -15.165750888 + 15 Combine like terms: -15 + 15 = 0 0 + x = -15.165750888 + 15 x = -15.165750888 + 15 Combine like terms: -15.165750888 + 15 = -0.165750888 x = -0.165750888 Simplifying x = -0.165750888Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.165750888, -0.165750888}
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