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Simplifying 5.4x2 + -2.7x + -15.4 = 0 Reorder the terms: -15.4 + -2.7x + 5.4x2 = 0 Solving -15.4 + -2.7x + 5.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.4 the coefficient of the squared term: Divide each side by '5.4'. -2.851851852 + -0.5x + x2 = 0 Move the constant term to the right: Add '2.851851852' to each side of the equation. -2.851851852 + -0.5x + 2.851851852 + x2 = 0 + 2.851851852 Reorder the terms: -2.851851852 + 2.851851852 + -0.5x + x2 = 0 + 2.851851852 Combine like terms: -2.851851852 + 2.851851852 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 2.851851852 -0.5x + x2 = 0 + 2.851851852 Combine like terms: 0 + 2.851851852 = 2.851851852 -0.5x + x2 = 2.851851852 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 2.851851852 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 2.851851852 + 0.0625 Combine like terms: 2.851851852 + 0.0625 = 2.914351852 0.0625 + -0.5x + x2 = 2.914351852 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 2.914351852 Calculate the square root of the right side: 1.707147285 Break this problem into two subproblems by setting (x + -0.25) equal to 1.707147285 and -1.707147285.Subproblem 1
x + -0.25 = 1.707147285 Simplifying x + -0.25 = 1.707147285 Reorder the terms: -0.25 + x = 1.707147285 Solving -0.25 + x = 1.707147285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.707147285 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.707147285 + 0.25 x = 1.707147285 + 0.25 Combine like terms: 1.707147285 + 0.25 = 1.957147285 x = 1.957147285 Simplifying x = 1.957147285Subproblem 2
x + -0.25 = -1.707147285 Simplifying x + -0.25 = -1.707147285 Reorder the terms: -0.25 + x = -1.707147285 Solving -0.25 + x = -1.707147285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.707147285 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.707147285 + 0.25 x = -1.707147285 + 0.25 Combine like terms: -1.707147285 + 0.25 = -1.457147285 x = -1.457147285 Simplifying x = -1.457147285Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.957147285, -1.457147285}
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