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Simplifying 82 = 14x + 4.9x2 Solving 82 = 14x + 4.9x2 Solving for variable 'x'. Reorder the terms: 82 + -14x + -4.9x2 = 14x + -14x + 4.9x2 + -4.9x2 Combine like terms: 14x + -14x = 0 82 + -14x + -4.9x2 = 0 + 4.9x2 + -4.9x2 82 + -14x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 82 + -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'. -16.73469388 + 2.857142857x + x2 = 0 Move the constant term to the right: Add '16.73469388' to each side of the equation. -16.73469388 + 2.857142857x + 16.73469388 + x2 = 0 + 16.73469388 Reorder the terms: -16.73469388 + 16.73469388 + 2.857142857x + x2 = 0 + 16.73469388 Combine like terms: -16.73469388 + 16.73469388 = 0.00000000 0.00000000 + 2.857142857x + x2 = 0 + 16.73469388 2.857142857x + x2 = 0 + 16.73469388 Combine like terms: 0 + 16.73469388 = 16.73469388 2.857142857x + x2 = 16.73469388 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 = 16.73469388 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857x + x2 = 16.73469388 + 2.040816328 Combine like terms: 16.73469388 + 2.040816328 = 18.775510208 2.040816328 + 2.857142857x + x2 = 18.775510208 Factor a perfect square on the left side: (x + 1.428571429)(x + 1.428571429) = 18.775510208 Calculate the square root of the right side: 4.333071683 Break this problem into two subproblems by setting (x + 1.428571429) equal to 4.333071683 and -4.333071683.Subproblem 1
x + 1.428571429 = 4.333071683 Simplifying x + 1.428571429 = 4.333071683 Reorder the terms: 1.428571429 + x = 4.333071683 Solving 1.428571429 + x = 4.333071683 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 = 4.333071683 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = 4.333071683 + -1.428571429 x = 4.333071683 + -1.428571429 Combine like terms: 4.333071683 + -1.428571429 = 2.904500254 x = 2.904500254 Simplifying x = 2.904500254Subproblem 2
x + 1.428571429 = -4.333071683 Simplifying x + 1.428571429 = -4.333071683 Reorder the terms: 1.428571429 + x = -4.333071683 Solving 1.428571429 + x = -4.333071683 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 = -4.333071683 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = -4.333071683 + -1.428571429 x = -4.333071683 + -1.428571429 Combine like terms: -4.333071683 + -1.428571429 = -5.761643112 x = -5.761643112 Simplifying x = -5.761643112Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.904500254, -5.761643112}
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