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Simplifying 4.9x2 + -14.7x + -10 = 0 Reorder the terms: -10 + -14.7x + 4.9x2 = 0 Solving -10 + -14.7x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -2.040816327 + -3x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -3x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -3x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -3x + x2 = 0 + 2.040816327 -3x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -3x + x2 = 2.040816327 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 2.040816327 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2.040816327 + 2.25 Combine like terms: 2.040816327 + 2.25 = 4.290816327 2.25 + -3x + x2 = 4.290816327 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4.290816327 Calculate the square root of the right side: 2.071428572 Break this problem into two subproblems by setting (x + -1.5) equal to 2.071428572 and -2.071428572.Subproblem 1
x + -1.5 = 2.071428572 Simplifying x + -1.5 = 2.071428572 Reorder the terms: -1.5 + x = 2.071428572 Solving -1.5 + x = 2.071428572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.071428572 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.071428572 + 1.5 x = 2.071428572 + 1.5 Combine like terms: 2.071428572 + 1.5 = 3.571428572 x = 3.571428572 Simplifying x = 3.571428572Subproblem 2
x + -1.5 = -2.071428572 Simplifying x + -1.5 = -2.071428572 Reorder the terms: -1.5 + x = -2.071428572 Solving -1.5 + x = -2.071428572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.071428572 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.071428572 + 1.5 x = -2.071428572 + 1.5 Combine like terms: -2.071428572 + 1.5 = -0.571428572 x = -0.571428572 Simplifying x = -0.571428572Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.571428572, -0.571428572}
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