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Simplifying 0 = 62 + 14x + -4.9x2 Solving 0 = 62 + 14x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -62 = -62 -62 + -14x + 4.9x2 = 62 + 14x + -4.9x2 + -62 + -14x + 4.9x2 Reorder the terms: -62 + -14x + 4.9x2 = 62 + -62 + 14x + -14x + -4.9x2 + 4.9x2 Combine like terms: 62 + -62 = 0 -62 + -14x + 4.9x2 = 0 + 14x + -14x + -4.9x2 + 4.9x2 -62 + -14x + 4.9x2 = 14x + -14x + -4.9x2 + 4.9x2 Combine like terms: 14x + -14x = 0 -62 + -14x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -62 + -14x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -62 + -14x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -12.65306122 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '12.65306122' to each side of the equation. -12.65306122 + -2.857142857x + 12.65306122 + x2 = 0 + 12.65306122 Reorder the terms: -12.65306122 + 12.65306122 + -2.857142857x + x2 = 0 + 12.65306122 Combine like terms: -12.65306122 + 12.65306122 = 0.00000000 0.00000000 + -2.857142857x + x2 = 0 + 12.65306122 -2.857142857x + x2 = 0 + 12.65306122 Combine like terms: 0 + 12.65306122 = 12.65306122 -2.857142857x + x2 = 12.65306122 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = 12.65306122 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 12.65306122 + 2.040816328 Combine like terms: 12.65306122 + 2.040816328 = 14.693877548 2.040816328 + -2.857142857x + x2 = 14.693877548 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 14.693877548 Calculate the square root of the right side: 3.83325939 Break this problem into two subproblems by setting (x + -1.428571429) equal to 3.83325939 and -3.83325939.Subproblem 1
x + -1.428571429 = 3.83325939 Simplifying x + -1.428571429 = 3.83325939 Reorder the terms: -1.428571429 + x = 3.83325939 Solving -1.428571429 + x = 3.83325939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 3.83325939 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 3.83325939 + 1.428571429 x = 3.83325939 + 1.428571429 Combine like terms: 3.83325939 + 1.428571429 = 5.261830819 x = 5.261830819 Simplifying x = 5.261830819Subproblem 2
x + -1.428571429 = -3.83325939 Simplifying x + -1.428571429 = -3.83325939 Reorder the terms: -1.428571429 + x = -3.83325939 Solving -1.428571429 + x = -3.83325939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -3.83325939 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -3.83325939 + 1.428571429 x = -3.83325939 + 1.428571429 Combine like terms: -3.83325939 + 1.428571429 = -2.404687961 x = -2.404687961 Simplifying x = -2.404687961Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.261830819, -2.404687961}
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