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Simplifying -4.9x2 + 94x + 297 = 0 Reorder the terms: 297 + 94x + -4.9x2 = 0 Solving 297 + 94x + -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'. -60.6122449 + -19.18367347x + x2 = 0 Move the constant term to the right: Add '60.6122449' to each side of the equation. -60.6122449 + -19.18367347x + 60.6122449 + x2 = 0 + 60.6122449 Reorder the terms: -60.6122449 + 60.6122449 + -19.18367347x + x2 = 0 + 60.6122449 Combine like terms: -60.6122449 + 60.6122449 = 0.0000000 0.0000000 + -19.18367347x + x2 = 0 + 60.6122449 -19.18367347x + x2 = 0 + 60.6122449 Combine like terms: 0 + 60.6122449 = 60.6122449 -19.18367347x + x2 = 60.6122449 The x term is -19.18367347x. Take half its coefficient (-9.591836735). Square it (92.00333195) and add it to both sides. Add '92.00333195' to each side of the equation. -19.18367347x + 92.00333195 + x2 = 60.6122449 + 92.00333195 Reorder the terms: 92.00333195 + -19.18367347x + x2 = 60.6122449 + 92.00333195 Combine like terms: 60.6122449 + 92.00333195 = 152.61557685 92.00333195 + -19.18367347x + x2 = 152.61557685 Factor a perfect square on the left side: (x + -9.591836735)(x + -9.591836735) = 152.61557685 Calculate the square root of the right side: 12.353767719 Break this problem into two subproblems by setting (x + -9.591836735) equal to 12.353767719 and -12.353767719.Subproblem 1
x + -9.591836735 = 12.353767719 Simplifying x + -9.591836735 = 12.353767719 Reorder the terms: -9.591836735 + x = 12.353767719 Solving -9.591836735 + x = 12.353767719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.591836735' to each side of the equation. -9.591836735 + 9.591836735 + x = 12.353767719 + 9.591836735 Combine like terms: -9.591836735 + 9.591836735 = 0.000000000 0.000000000 + x = 12.353767719 + 9.591836735 x = 12.353767719 + 9.591836735 Combine like terms: 12.353767719 + 9.591836735 = 21.945604454 x = 21.945604454 Simplifying x = 21.945604454Subproblem 2
x + -9.591836735 = -12.353767719 Simplifying x + -9.591836735 = -12.353767719 Reorder the terms: -9.591836735 + x = -12.353767719 Solving -9.591836735 + x = -12.353767719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.591836735' to each side of the equation. -9.591836735 + 9.591836735 + x = -12.353767719 + 9.591836735 Combine like terms: -9.591836735 + 9.591836735 = 0.000000000 0.000000000 + x = -12.353767719 + 9.591836735 x = -12.353767719 + 9.591836735 Combine like terms: -12.353767719 + 9.591836735 = -2.761930984 x = -2.761930984 Simplifying x = -2.761930984Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.945604454, -2.761930984}
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