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Simplifying -5(3c + -9) + -9c + -7c2 + 5 = 0 Reorder the terms: -5(-9 + 3c) + -9c + -7c2 + 5 = 0 (-9 * -5 + 3c * -5) + -9c + -7c2 + 5 = 0 (45 + -15c) + -9c + -7c2 + 5 = 0 Reorder the terms: 45 + 5 + -15c + -9c + -7c2 = 0 Combine like terms: 45 + 5 = 50 50 + -15c + -9c + -7c2 = 0 Combine like terms: -15c + -9c = -24c 50 + -24c + -7c2 = 0 Solving 50 + -24c + -7c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -7.142857143 + 3.428571429c + c2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + 3.428571429c + 7.142857143 + c2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + 3.428571429c + c2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + 3.428571429c + c2 = 0 + 7.142857143 3.428571429c + c2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 3.428571429c + c2 = 7.142857143 The c term is 3.428571429c. Take half its coefficient (1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. 3.428571429c + 2.938775513 + c2 = 7.142857143 + 2.938775513 Reorder the terms: 2.938775513 + 3.428571429c + c2 = 7.142857143 + 2.938775513 Combine like terms: 7.142857143 + 2.938775513 = 10.081632656 2.938775513 + 3.428571429c + c2 = 10.081632656 Factor a perfect square on the left side: (c + 1.714285715)(c + 1.714285715) = 10.081632656 Calculate the square root of the right side: 3.175158682 Break this problem into two subproblems by setting (c + 1.714285715) equal to 3.175158682 and -3.175158682.Subproblem 1
c + 1.714285715 = 3.175158682 Simplifying c + 1.714285715 = 3.175158682 Reorder the terms: 1.714285715 + c = 3.175158682 Solving 1.714285715 + c = 3.175158682 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.714285715' to each side of the equation. 1.714285715 + -1.714285715 + c = 3.175158682 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + c = 3.175158682 + -1.714285715 c = 3.175158682 + -1.714285715 Combine like terms: 3.175158682 + -1.714285715 = 1.460872967 c = 1.460872967 Simplifying c = 1.460872967Subproblem 2
c + 1.714285715 = -3.175158682 Simplifying c + 1.714285715 = -3.175158682 Reorder the terms: 1.714285715 + c = -3.175158682 Solving 1.714285715 + c = -3.175158682 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.714285715' to each side of the equation. 1.714285715 + -1.714285715 + c = -3.175158682 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + c = -3.175158682 + -1.714285715 c = -3.175158682 + -1.714285715 Combine like terms: -3.175158682 + -1.714285715 = -4.889444397 c = -4.889444397 Simplifying c = -4.889444397Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.460872967, -4.889444397}
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