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Simplifying 9x2 + 20x = 158 Reorder the terms: 20x + 9x2 = 158 Solving 20x + 9x2 = 158 Solving for variable 'x'. Reorder the terms: -158 + 20x + 9x2 = 158 + -158 Combine like terms: 158 + -158 = 0 -158 + 20x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -17.55555556 + 2.222222222x + x2 = 0 Move the constant term to the right: Add '17.55555556' to each side of the equation. -17.55555556 + 2.222222222x + 17.55555556 + x2 = 0 + 17.55555556 Reorder the terms: -17.55555556 + 17.55555556 + 2.222222222x + x2 = 0 + 17.55555556 Combine like terms: -17.55555556 + 17.55555556 = 0.00000000 0.00000000 + 2.222222222x + x2 = 0 + 17.55555556 2.222222222x + x2 = 0 + 17.55555556 Combine like terms: 0 + 17.55555556 = 17.55555556 2.222222222x + x2 = 17.55555556 The x term is 2.222222222x. Take half its coefficient (1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. 2.222222222x + 1.234567901 + x2 = 17.55555556 + 1.234567901 Reorder the terms: 1.234567901 + 2.222222222x + x2 = 17.55555556 + 1.234567901 Combine like terms: 17.55555556 + 1.234567901 = 18.790123461 1.234567901 + 2.222222222x + x2 = 18.790123461 Factor a perfect square on the left side: (x + 1.111111111)(x + 1.111111111) = 18.790123461 Calculate the square root of the right side: 4.334757601 Break this problem into two subproblems by setting (x + 1.111111111) equal to 4.334757601 and -4.334757601.Subproblem 1
x + 1.111111111 = 4.334757601 Simplifying x + 1.111111111 = 4.334757601 Reorder the terms: 1.111111111 + x = 4.334757601 Solving 1.111111111 + x = 4.334757601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = 4.334757601 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = 4.334757601 + -1.111111111 x = 4.334757601 + -1.111111111 Combine like terms: 4.334757601 + -1.111111111 = 3.22364649 x = 3.22364649 Simplifying x = 3.22364649Subproblem 2
x + 1.111111111 = -4.334757601 Simplifying x + 1.111111111 = -4.334757601 Reorder the terms: 1.111111111 + x = -4.334757601 Solving 1.111111111 + x = -4.334757601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = -4.334757601 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = -4.334757601 + -1.111111111 x = -4.334757601 + -1.111111111 Combine like terms: -4.334757601 + -1.111111111 = -5.445868712 x = -5.445868712 Simplifying x = -5.445868712Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.22364649, -5.445868712}
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