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Simplifying 81 + 30x + -1x2 = 0 Solving 81 + 30x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -81 + -30x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + -30x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -30x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -30x + x2 = 0 + 81 -30x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -30x + x2 = 81 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 = 81 + 225 Reorder the terms: 225 + -30x + x2 = 81 + 225 Combine like terms: 81 + 225 = 306 225 + -30x + x2 = 306 Factor a perfect square on the left side: (x + -15)(x + -15) = 306 Calculate the square root of the right side: 17.492855685 Break this problem into two subproblems by setting (x + -15) equal to 17.492855685 and -17.492855685.Subproblem 1
x + -15 = 17.492855685 Simplifying x + -15 = 17.492855685 Reorder the terms: -15 + x = 17.492855685 Solving -15 + x = 17.492855685 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 = 17.492855685 + 15 Combine like terms: -15 + 15 = 0 0 + x = 17.492855685 + 15 x = 17.492855685 + 15 Combine like terms: 17.492855685 + 15 = 32.492855685 x = 32.492855685 Simplifying x = 32.492855685Subproblem 2
x + -15 = -17.492855685 Simplifying x + -15 = -17.492855685 Reorder the terms: -15 + x = -17.492855685 Solving -15 + x = -17.492855685 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 = -17.492855685 + 15 Combine like terms: -15 + 15 = 0 0 + x = -17.492855685 + 15 x = -17.492855685 + 15 Combine like terms: -17.492855685 + 15 = -2.492855685 x = -2.492855685 Simplifying x = -2.492855685Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.492855685, -2.492855685}
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