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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 = 0.209183673 2.25 + -3x + x2 = 0.209183673 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.209183673 Calculate the square root of the right side: 0.457366016 Break this problem into two subproblems by setting (x + -1.5) equal to 0.457366016 and -0.457366016.Subproblem 1
x + -1.5 = 0.457366016 Simplifying x + -1.5 = 0.457366016 Reorder the terms: -1.5 + x = 0.457366016 Solving -1.5 + x = 0.457366016 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 = 0.457366016 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.457366016 + 1.5 x = 0.457366016 + 1.5 Combine like terms: 0.457366016 + 1.5 = 1.957366016 x = 1.957366016 Simplifying x = 1.957366016Subproblem 2
x + -1.5 = -0.457366016 Simplifying x + -1.5 = -0.457366016 Reorder the terms: -1.5 + x = -0.457366016 Solving -1.5 + x = -0.457366016 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 = -0.457366016 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.457366016 + 1.5 x = -0.457366016 + 1.5 Combine like terms: -0.457366016 + 1.5 = 1.042633984 x = 1.042633984 Simplifying x = 1.042633984Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.957366016, 1.042633984}
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