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Simplifying 2.4x2 + -5.1x + 3 = 12.7 Reorder the terms: 3 + -5.1x + 2.4x2 = 12.7 Solving 3 + -5.1x + 2.4x2 = 12.7 Solving for variable 'x'. Reorder the terms: 3 + -12.7 + -5.1x + 2.4x2 = 12.7 + -12.7 Combine like terms: 3 + -12.7 = -9.7 -9.7 + -5.1x + 2.4x2 = 12.7 + -12.7 Combine like terms: 12.7 + -12.7 = 0.0 -9.7 + -5.1x + 2.4x2 = 0.0 Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. -4.041666667 + -2.125x + x2 = 0 Move the constant term to the right: Add '4.041666667' to each side of the equation. -4.041666667 + -2.125x + 4.041666667 + x2 = 0 + 4.041666667 Reorder the terms: -4.041666667 + 4.041666667 + -2.125x + x2 = 0 + 4.041666667 Combine like terms: -4.041666667 + 4.041666667 = 0.000000000 0.000000000 + -2.125x + x2 = 0 + 4.041666667 -2.125x + x2 = 0 + 4.041666667 Combine like terms: 0 + 4.041666667 = 4.041666667 -2.125x + x2 = 4.041666667 The x term is -2.125x. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125x + 1.12890625 + x2 = 4.041666667 + 1.12890625 Reorder the terms: 1.12890625 + -2.125x + x2 = 4.041666667 + 1.12890625 Combine like terms: 4.041666667 + 1.12890625 = 5.170572917 1.12890625 + -2.125x + x2 = 5.170572917 Factor a perfect square on the left side: (x + -1.0625)(x + -1.0625) = 5.170572917 Calculate the square root of the right side: 2.273889381 Break this problem into two subproblems by setting (x + -1.0625) equal to 2.273889381 and -2.273889381.Subproblem 1
x + -1.0625 = 2.273889381 Simplifying x + -1.0625 = 2.273889381 Reorder the terms: -1.0625 + x = 2.273889381 Solving -1.0625 + x = 2.273889381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = 2.273889381 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = 2.273889381 + 1.0625 x = 2.273889381 + 1.0625 Combine like terms: 2.273889381 + 1.0625 = 3.336389381 x = 3.336389381 Simplifying x = 3.336389381Subproblem 2
x + -1.0625 = -2.273889381 Simplifying x + -1.0625 = -2.273889381 Reorder the terms: -1.0625 + x = -2.273889381 Solving -1.0625 + x = -2.273889381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = -2.273889381 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = -2.273889381 + 1.0625 x = -2.273889381 + 1.0625 Combine like terms: -2.273889381 + 1.0625 = -1.211389381 x = -1.211389381 Simplifying x = -1.211389381Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.336389381, -1.211389381}
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