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Simplifying x2 + -30x + 27 = 0 Reorder the terms: 27 + -30x + x2 = 0 Solving 27 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -30x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -30x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -30x + x2 = 0 + -27 -30x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -30x + x2 = -27 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 = -27 + 225 Reorder the terms: 225 + -30x + x2 = -27 + 225 Combine like terms: -27 + 225 = 198 225 + -30x + x2 = 198 Factor a perfect square on the left side: (x + -15)(x + -15) = 198 Calculate the square root of the right side: 14.071247279 Break this problem into two subproblems by setting (x + -15) equal to 14.071247279 and -14.071247279.Subproblem 1
x + -15 = 14.071247279 Simplifying x + -15 = 14.071247279 Reorder the terms: -15 + x = 14.071247279 Solving -15 + x = 14.071247279 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 = 14.071247279 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.071247279 + 15 x = 14.071247279 + 15 Combine like terms: 14.071247279 + 15 = 29.071247279 x = 29.071247279 Simplifying x = 29.071247279Subproblem 2
x + -15 = -14.071247279 Simplifying x + -15 = -14.071247279 Reorder the terms: -15 + x = -14.071247279 Solving -15 + x = -14.071247279 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 = -14.071247279 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.071247279 + 15 x = -14.071247279 + 15 Combine like terms: -14.071247279 + 15 = 0.928752721 x = 0.928752721 Simplifying x = 0.928752721Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.071247279, 0.928752721}
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