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Simplifying x2 + -30x + -315 = 0 Reorder the terms: -315 + -30x + x2 = 0 Solving -315 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '315' to each side of the equation. -315 + -30x + 315 + x2 = 0 + 315 Reorder the terms: -315 + 315 + -30x + x2 = 0 + 315 Combine like terms: -315 + 315 = 0 0 + -30x + x2 = 0 + 315 -30x + x2 = 0 + 315 Combine like terms: 0 + 315 = 315 -30x + x2 = 315 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 = 315 + 225 Reorder the terms: 225 + -30x + x2 = 315 + 225 Combine like terms: 315 + 225 = 540 225 + -30x + x2 = 540 Factor a perfect square on the left side: (x + -15)(x + -15) = 540 Calculate the square root of the right side: 23.237900077 Break this problem into two subproblems by setting (x + -15) equal to 23.237900077 and -23.237900077.Subproblem 1
x + -15 = 23.237900077 Simplifying x + -15 = 23.237900077 Reorder the terms: -15 + x = 23.237900077 Solving -15 + x = 23.237900077 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 = 23.237900077 + 15 Combine like terms: -15 + 15 = 0 0 + x = 23.237900077 + 15 x = 23.237900077 + 15 Combine like terms: 23.237900077 + 15 = 38.237900077 x = 38.237900077 Simplifying x = 38.237900077Subproblem 2
x + -15 = -23.237900077 Simplifying x + -15 = -23.237900077 Reorder the terms: -15 + x = -23.237900077 Solving -15 + x = -23.237900077 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 = -23.237900077 + 15 Combine like terms: -15 + 15 = 0 0 + x = -23.237900077 + 15 x = -23.237900077 + 15 Combine like terms: -23.237900077 + 15 = -8.237900077 x = -8.237900077 Simplifying x = -8.237900077Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.237900077, -8.237900077}
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