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Simplifying -65 = 14x + -0.5(9.8)(x2) Multiply -0.5 * 9.8 -65 = 14x + -4.9x2 Solving -65 = 14x + -4.9x2 Solving for variable 'x'. Reorder the terms: -65 + -14x + 4.9x2 = 14x + -14x + -4.9x2 + 4.9x2 Combine like terms: 14x + -14x = 0 -65 + -14x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -65 + -14x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -65 + -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'. -13.26530612 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '13.26530612' to each side of the equation. -13.26530612 + -2.857142857x + 13.26530612 + x2 = 0 + 13.26530612 Reorder the terms: -13.26530612 + 13.26530612 + -2.857142857x + x2 = 0 + 13.26530612 Combine like terms: -13.26530612 + 13.26530612 = 0.00000000 0.00000000 + -2.857142857x + x2 = 0 + 13.26530612 -2.857142857x + x2 = 0 + 13.26530612 Combine like terms: 0 + 13.26530612 = 13.26530612 -2.857142857x + x2 = 13.26530612 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 = 13.26530612 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 13.26530612 + 2.040816328 Combine like terms: 13.26530612 + 2.040816328 = 15.306122448 2.040816328 + -2.857142857x + x2 = 15.306122448 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 15.306122448 Calculate the square root of the right side: 3.912303982 Break this problem into two subproblems by setting (x + -1.428571429) equal to 3.912303982 and -3.912303982.Subproblem 1
x + -1.428571429 = 3.912303982 Simplifying x + -1.428571429 = 3.912303982 Reorder the terms: -1.428571429 + x = 3.912303982 Solving -1.428571429 + x = 3.912303982 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 = 3.912303982 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 3.912303982 + 1.428571429 x = 3.912303982 + 1.428571429 Combine like terms: 3.912303982 + 1.428571429 = 5.340875411 x = 5.340875411 Simplifying x = 5.340875411Subproblem 2
x + -1.428571429 = -3.912303982 Simplifying x + -1.428571429 = -3.912303982 Reorder the terms: -1.428571429 + x = -3.912303982 Solving -1.428571429 + x = -3.912303982 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 = -3.912303982 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -3.912303982 + 1.428571429 x = -3.912303982 + 1.428571429 Combine like terms: -3.912303982 + 1.428571429 = -2.483732553 x = -2.483732553 Simplifying x = -2.483732553Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.340875411, -2.483732553}
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