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Simplifying 10 = -9.6x2 + 30x + 20 Reorder the terms: 10 = 20 + 30x + -9.6x2 Solving 10 = 20 + 30x + -9.6x2 Solving for variable 'x'. Combine like terms: 10 + -20 = -10 -10 + -30x + 9.6x2 = 20 + 30x + -9.6x2 + -20 + -30x + 9.6x2 Reorder the terms: -10 + -30x + 9.6x2 = 20 + -20 + 30x + -30x + -9.6x2 + 9.6x2 Combine like terms: 20 + -20 = 0 -10 + -30x + 9.6x2 = 0 + 30x + -30x + -9.6x2 + 9.6x2 -10 + -30x + 9.6x2 = 30x + -30x + -9.6x2 + 9.6x2 Combine like terms: 30x + -30x = 0 -10 + -30x + 9.6x2 = 0 + -9.6x2 + 9.6x2 -10 + -30x + 9.6x2 = -9.6x2 + 9.6x2 Combine like terms: -9.6x2 + 9.6x2 = 0.0 -10 + -30x + 9.6x2 = 0.0 Begin completing the square. Divide all terms by 9.6 the coefficient of the squared term: Divide each side by '9.6'. -1.041666667 + -3.125x + x2 = 0 Move the constant term to the right: Add '1.041666667' to each side of the equation. -1.041666667 + -3.125x + 1.041666667 + x2 = 0 + 1.041666667 Reorder the terms: -1.041666667 + 1.041666667 + -3.125x + x2 = 0 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + -3.125x + x2 = 0 + 1.041666667 -3.125x + x2 = 0 + 1.041666667 Combine like terms: 0 + 1.041666667 = 1.041666667 -3.125x + x2 = 1.041666667 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 1.041666667 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 1.041666667 + 2.44140625 Combine like terms: 1.041666667 + 2.44140625 = 3.483072917 2.44140625 + -3.125x + x2 = 3.483072917 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 3.483072917 Calculate the square root of the right side: 1.866299257 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.866299257 and -1.866299257.Subproblem 1
x + -1.5625 = 1.866299257 Simplifying x + -1.5625 = 1.866299257 Reorder the terms: -1.5625 + x = 1.866299257 Solving -1.5625 + x = 1.866299257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.866299257 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.866299257 + 1.5625 x = 1.866299257 + 1.5625 Combine like terms: 1.866299257 + 1.5625 = 3.428799257 x = 3.428799257 Simplifying x = 3.428799257Subproblem 2
x + -1.5625 = -1.866299257 Simplifying x + -1.5625 = -1.866299257 Reorder the terms: -1.5625 + x = -1.866299257 Solving -1.5625 + x = -1.866299257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.866299257 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.866299257 + 1.5625 x = -1.866299257 + 1.5625 Combine like terms: -1.866299257 + 1.5625 = -0.303799257 x = -0.303799257 Simplifying x = -0.303799257Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.428799257, -0.303799257}
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