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Simplifying 7x2 + 58x + 16 = 490 Reorder the terms: 16 + 58x + 7x2 = 490 Solving 16 + 58x + 7x2 = 490 Solving for variable 'x'. Reorder the terms: 16 + -490 + 58x + 7x2 = 490 + -490 Combine like terms: 16 + -490 = -474 -474 + 58x + 7x2 = 490 + -490 Combine like terms: 490 + -490 = 0 -474 + 58x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -67.71428571 + 8.285714286x + x2 = 0 Move the constant term to the right: Add '67.71428571' to each side of the equation. -67.71428571 + 8.285714286x + 67.71428571 + x2 = 0 + 67.71428571 Reorder the terms: -67.71428571 + 67.71428571 + 8.285714286x + x2 = 0 + 67.71428571 Combine like terms: -67.71428571 + 67.71428571 = 0.00000000 0.00000000 + 8.285714286x + x2 = 0 + 67.71428571 8.285714286x + x2 = 0 + 67.71428571 Combine like terms: 0 + 67.71428571 = 67.71428571 8.285714286x + x2 = 67.71428571 The x term is 8.285714286x. Take half its coefficient (4.142857143). Square it (17.16326531) and add it to both sides. Add '17.16326531' to each side of the equation. 8.285714286x + 17.16326531 + x2 = 67.71428571 + 17.16326531 Reorder the terms: 17.16326531 + 8.285714286x + x2 = 67.71428571 + 17.16326531 Combine like terms: 67.71428571 + 17.16326531 = 84.87755102 17.16326531 + 8.285714286x + x2 = 84.87755102 Factor a perfect square on the left side: (x + 4.142857143)(x + 4.142857143) = 84.87755102 Calculate the square root of the right side: 9.212901336 Break this problem into two subproblems by setting (x + 4.142857143) equal to 9.212901336 and -9.212901336.Subproblem 1
x + 4.142857143 = 9.212901336 Simplifying x + 4.142857143 = 9.212901336 Reorder the terms: 4.142857143 + x = 9.212901336 Solving 4.142857143 + x = 9.212901336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.142857143' to each side of the equation. 4.142857143 + -4.142857143 + x = 9.212901336 + -4.142857143 Combine like terms: 4.142857143 + -4.142857143 = 0.000000000 0.000000000 + x = 9.212901336 + -4.142857143 x = 9.212901336 + -4.142857143 Combine like terms: 9.212901336 + -4.142857143 = 5.070044193 x = 5.070044193 Simplifying x = 5.070044193Subproblem 2
x + 4.142857143 = -9.212901336 Simplifying x + 4.142857143 = -9.212901336 Reorder the terms: 4.142857143 + x = -9.212901336 Solving 4.142857143 + x = -9.212901336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.142857143' to each side of the equation. 4.142857143 + -4.142857143 + x = -9.212901336 + -4.142857143 Combine like terms: 4.142857143 + -4.142857143 = 0.000000000 0.000000000 + x = -9.212901336 + -4.142857143 x = -9.212901336 + -4.142857143 Combine like terms: -9.212901336 + -4.142857143 = -13.355758479 x = -13.355758479 Simplifying x = -13.355758479Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.070044193, -13.355758479}
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