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Simplifying 3x2 + -104.40x + 896.28 = 0 Reorder the terms: 896.28 + -104.40x + 3x2 = 0 Solving 896.28 + -104.40x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 298.76 + -34.8x + x2 = 0 Move the constant term to the right: Add '-298.76' to each side of the equation. 298.76 + -34.8x + -298.76 + x2 = 0 + -298.76 Reorder the terms: 298.76 + -298.76 + -34.8x + x2 = 0 + -298.76 Combine like terms: 298.76 + -298.76 = 0.00 0.00 + -34.8x + x2 = 0 + -298.76 -34.8x + x2 = 0 + -298.76 Combine like terms: 0 + -298.76 = -298.76 -34.8x + x2 = -298.76 The x term is -34.8x. Take half its coefficient (-17.4). Square it (302.76) and add it to both sides. Add '302.76' to each side of the equation. -34.8x + 302.76 + x2 = -298.76 + 302.76 Reorder the terms: 302.76 + -34.8x + x2 = -298.76 + 302.76 Combine like terms: -298.76 + 302.76 = 4 302.76 + -34.8x + x2 = 4 Factor a perfect square on the left side: (x + -17.4)(x + -17.4) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -17.4) equal to 2 and -2.Subproblem 1
x + -17.4 = 2 Simplifying x + -17.4 = 2 Reorder the terms: -17.4 + x = 2 Solving -17.4 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.4' to each side of the equation. -17.4 + 17.4 + x = 2 + 17.4 Combine like terms: -17.4 + 17.4 = 0.0 0.0 + x = 2 + 17.4 x = 2 + 17.4 Combine like terms: 2 + 17.4 = 19.4 x = 19.4 Simplifying x = 19.4Subproblem 2
x + -17.4 = -2 Simplifying x + -17.4 = -2 Reorder the terms: -17.4 + x = -2 Solving -17.4 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.4' to each side of the equation. -17.4 + 17.4 + x = -2 + 17.4 Combine like terms: -17.4 + 17.4 = 0.0 0.0 + x = -2 + 17.4 x = -2 + 17.4 Combine like terms: -2 + 17.4 = 15.4 x = 15.4 Simplifying x = 15.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.4, 15.4}
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