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Simplifying 0.5x2 + -15x + -100 = 0 Reorder the terms: -100 + -15x + 0.5x2 = 0 Solving -100 + -15x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -200 + -30x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -30x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -30x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -30x + x2 = 0 + 200 -30x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -30x + x2 = 200 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 = 200 + 225 Reorder the terms: 225 + -30x + x2 = 200 + 225 Combine like terms: 200 + 225 = 425 225 + -30x + x2 = 425 Factor a perfect square on the left side: (x + -15)(x + -15) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (x + -15) equal to 20.615528128 and -20.615528128.Subproblem 1
x + -15 = 20.615528128 Simplifying x + -15 = 20.615528128 Reorder the terms: -15 + x = 20.615528128 Solving -15 + x = 20.615528128 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 = 20.615528128 + 15 Combine like terms: -15 + 15 = 0 0 + x = 20.615528128 + 15 x = 20.615528128 + 15 Combine like terms: 20.615528128 + 15 = 35.615528128 x = 35.615528128 Simplifying x = 35.615528128Subproblem 2
x + -15 = -20.615528128 Simplifying x + -15 = -20.615528128 Reorder the terms: -15 + x = -20.615528128 Solving -15 + x = -20.615528128 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 = -20.615528128 + 15 Combine like terms: -15 + 15 = 0 0 + x = -20.615528128 + 15 x = -20.615528128 + 15 Combine like terms: -20.615528128 + 15 = -5.615528128 x = -5.615528128 Simplifying x = -5.615528128Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.615528128, -5.615528128}
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