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Simplifying 2.73x2 + 1.47x + -5.72 = 0 Reorder the terms: -5.72 + 1.47x + 2.73x2 = 0 Solving -5.72 + 1.47x + 2.73x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.73 the coefficient of the squared term: Divide each side by '2.73'. -2.095238095 + 0.5384615385x + x2 = 0 Move the constant term to the right: Add '2.095238095' to each side of the equation. -2.095238095 + 0.5384615385x + 2.095238095 + x2 = 0 + 2.095238095 Reorder the terms: -2.095238095 + 2.095238095 + 0.5384615385x + x2 = 0 + 2.095238095 Combine like terms: -2.095238095 + 2.095238095 = 0.000000000 0.000000000 + 0.5384615385x + x2 = 0 + 2.095238095 0.5384615385x + x2 = 0 + 2.095238095 Combine like terms: 0 + 2.095238095 = 2.095238095 0.5384615385x + x2 = 2.095238095 The x term is 0.5384615385x. Take half its coefficient (0.2692307693). Square it (0.07248520714) and add it to both sides. Add '0.07248520714' to each side of the equation. 0.5384615385x + 0.07248520714 + x2 = 2.095238095 + 0.07248520714 Reorder the terms: 0.07248520714 + 0.5384615385x + x2 = 2.095238095 + 0.07248520714 Combine like terms: 2.095238095 + 0.07248520714 = 2.16772330214 0.07248520714 + 0.5384615385x + x2 = 2.16772330214 Factor a perfect square on the left side: (x + 0.2692307693)(x + 0.2692307693) = 2.16772330214 Calculate the square root of the right side: 1.472319022 Break this problem into two subproblems by setting (x + 0.2692307693) equal to 1.472319022 and -1.472319022.Subproblem 1
x + 0.2692307693 = 1.472319022 Simplifying x + 0.2692307693 = 1.472319022 Reorder the terms: 0.2692307693 + x = 1.472319022 Solving 0.2692307693 + x = 1.472319022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = 1.472319022 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = 1.472319022 + -0.2692307693 x = 1.472319022 + -0.2692307693 Combine like terms: 1.472319022 + -0.2692307693 = 1.2030882527 x = 1.2030882527 Simplifying x = 1.2030882527Subproblem 2
x + 0.2692307693 = -1.472319022 Simplifying x + 0.2692307693 = -1.472319022 Reorder the terms: 0.2692307693 + x = -1.472319022 Solving 0.2692307693 + x = -1.472319022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = -1.472319022 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = -1.472319022 + -0.2692307693 x = -1.472319022 + -0.2692307693 Combine like terms: -1.472319022 + -0.2692307693 = -1.7415497913 x = -1.7415497913 Simplifying x = -1.7415497913Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2030882527, -1.7415497913}
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