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Simplifying x2 + -30x + 6 = 0 Reorder the terms: 6 + -30x + x2 = 0 Solving 6 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -30x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -30x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -30x + x2 = 0 + -6 -30x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -30x + x2 = -6 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 = -6 + 225 Reorder the terms: 225 + -30x + x2 = -6 + 225 Combine like terms: -6 + 225 = 219 225 + -30x + x2 = 219 Factor a perfect square on the left side: (x + -15)(x + -15) = 219 Calculate the square root of the right side: 14.798648587 Break this problem into two subproblems by setting (x + -15) equal to 14.798648587 and -14.798648587.Subproblem 1
x + -15 = 14.798648587 Simplifying x + -15 = 14.798648587 Reorder the terms: -15 + x = 14.798648587 Solving -15 + x = 14.798648587 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 = 14.798648587 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.798648587 + 15 x = 14.798648587 + 15 Combine like terms: 14.798648587 + 15 = 29.798648587 x = 29.798648587 Simplifying x = 29.798648587Subproblem 2
x + -15 = -14.798648587 Simplifying x + -15 = -14.798648587 Reorder the terms: -15 + x = -14.798648587 Solving -15 + x = -14.798648587 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 = -14.798648587 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.798648587 + 15 x = -14.798648587 + 15 Combine like terms: -14.798648587 + 15 = 0.201351413 x = 0.201351413 Simplifying x = 0.201351413Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.798648587, 0.201351413}
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