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Simplifying 0.1x2 + -2x + 3 = 0 Reorder the terms: 3 + -2x + 0.1x2 = 0 Solving 3 + -2x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 30 + -20x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -20x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -20x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -20x + x2 = 0 + -30 -20x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -20x + x2 = -30 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 = -30 + 100 Reorder the terms: 100 + -20x + x2 = -30 + 100 Combine like terms: -30 + 100 = 70 100 + -20x + x2 = 70 Factor a perfect square on the left side: (x + -10)(x + -10) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + -10) equal to 8.366600265 and -8.366600265.Subproblem 1
x + -10 = 8.366600265 Simplifying x + -10 = 8.366600265 Reorder the terms: -10 + x = 8.366600265 Solving -10 + x = 8.366600265 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 = 8.366600265 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.366600265 + 10 x = 8.366600265 + 10 Combine like terms: 8.366600265 + 10 = 18.366600265 x = 18.366600265 Simplifying x = 18.366600265Subproblem 2
x + -10 = -8.366600265 Simplifying x + -10 = -8.366600265 Reorder the terms: -10 + x = -8.366600265 Solving -10 + x = -8.366600265 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 = -8.366600265 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.366600265 + 10 x = -8.366600265 + 10 Combine like terms: -8.366600265 + 10 = 1.633399735 x = 1.633399735 Simplifying x = 1.633399735Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.366600265, 1.633399735}
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