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Simplifying 10x2 + -3x + -102 = 0 Reorder the terms: -102 + -3x + 10x2 = 0 Solving -102 + -3x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -10.2 + -0.3x + x2 = 0 Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + -0.3x + 10.2 + x2 = 0 + 10.2 Reorder the terms: -10.2 + 10.2 + -0.3x + x2 = 0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + -0.3x + x2 = 0 + 10.2 -0.3x + x2 = 0 + 10.2 Combine like terms: 0 + 10.2 = 10.2 -0.3x + x2 = 10.2 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 10.2 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 10.2 + 0.0225 Combine like terms: 10.2 + 0.0225 = 10.2225 0.0225 + -0.3x + x2 = 10.2225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 10.2225 Calculate the square root of the right side: 3.197264456 Break this problem into two subproblems by setting (x + -0.15) equal to 3.197264456 and -3.197264456.Subproblem 1
x + -0.15 = 3.197264456 Simplifying x + -0.15 = 3.197264456 Reorder the terms: -0.15 + x = 3.197264456 Solving -0.15 + x = 3.197264456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 3.197264456 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 3.197264456 + 0.15 x = 3.197264456 + 0.15 Combine like terms: 3.197264456 + 0.15 = 3.347264456 x = 3.347264456 Simplifying x = 3.347264456Subproblem 2
x + -0.15 = -3.197264456 Simplifying x + -0.15 = -3.197264456 Reorder the terms: -0.15 + x = -3.197264456 Solving -0.15 + x = -3.197264456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -3.197264456 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -3.197264456 + 0.15 x = -3.197264456 + 0.15 Combine like terms: -3.197264456 + 0.15 = -3.047264456 x = -3.047264456 Simplifying x = -3.047264456Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.347264456, -3.047264456}
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