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Simplifying 0.5x2 + 10x + -17.2 = 0 Reorder the terms: -17.2 + 10x + 0.5x2 = 0 Solving -17.2 + 10x + 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'. -34.4 + 20x + x2 = 0 Move the constant term to the right: Add '34.4' to each side of the equation. -34.4 + 20x + 34.4 + x2 = 0 + 34.4 Reorder the terms: -34.4 + 34.4 + 20x + x2 = 0 + 34.4 Combine like terms: -34.4 + 34.4 = 0.0 0.0 + 20x + x2 = 0 + 34.4 20x + x2 = 0 + 34.4 Combine like terms: 0 + 34.4 = 34.4 20x + x2 = 34.4 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 34.4 + 100 Reorder the terms: 100 + 20x + x2 = 34.4 + 100 Combine like terms: 34.4 + 100 = 134.4 100 + 20x + x2 = 134.4 Factor a perfect square on the left side: (x + 10)(x + 10) = 134.4 Calculate the square root of the right side: 11.593101397 Break this problem into two subproblems by setting (x + 10) equal to 11.593101397 and -11.593101397.Subproblem 1
x + 10 = 11.593101397 Simplifying x + 10 = 11.593101397 Reorder the terms: 10 + x = 11.593101397 Solving 10 + x = 11.593101397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.593101397 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.593101397 + -10 x = 11.593101397 + -10 Combine like terms: 11.593101397 + -10 = 1.593101397 x = 1.593101397 Simplifying x = 1.593101397Subproblem 2
x + 10 = -11.593101397 Simplifying x + 10 = -11.593101397 Reorder the terms: 10 + x = -11.593101397 Solving 10 + x = -11.593101397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.593101397 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.593101397 + -10 x = -11.593101397 + -10 Combine like terms: -11.593101397 + -10 = -21.593101397 x = -21.593101397 Simplifying x = -21.593101397Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.593101397, -21.593101397}
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