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Simplifying 7x2 + 18x + -36 = 0 Reorder the terms: -36 + 18x + 7x2 = 0 Solving -36 + 18x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.142857143 + 2.571428571x + x2 = 0 Move the constant term to the right: Add '5.142857143' to each side of the equation. -5.142857143 + 2.571428571x + 5.142857143 + x2 = 0 + 5.142857143 Reorder the terms: -5.142857143 + 5.142857143 + 2.571428571x + x2 = 0 + 5.142857143 Combine like terms: -5.142857143 + 5.142857143 = 0.000000000 0.000000000 + 2.571428571x + x2 = 0 + 5.142857143 2.571428571x + x2 = 0 + 5.142857143 Combine like terms: 0 + 5.142857143 = 5.142857143 2.571428571x + x2 = 5.142857143 The x term is 2.571428571x. Take half its coefficient (1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. 2.571428571x + 1.653061225 + x2 = 5.142857143 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = 5.142857143 + 1.653061225 Combine like terms: 5.142857143 + 1.653061225 = 6.795918368 1.653061225 + 2.571428571x + x2 = 6.795918368 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = 6.795918368 Calculate the square root of the right side: 2.606898227 Break this problem into two subproblems by setting (x + 1.285714286) equal to 2.606898227 and -2.606898227.Subproblem 1
x + 1.285714286 = 2.606898227 Simplifying x + 1.285714286 = 2.606898227 Reorder the terms: 1.285714286 + x = 2.606898227 Solving 1.285714286 + x = 2.606898227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = 2.606898227 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = 2.606898227 + -1.285714286 x = 2.606898227 + -1.285714286 Combine like terms: 2.606898227 + -1.285714286 = 1.321183941 x = 1.321183941 Simplifying x = 1.321183941Subproblem 2
x + 1.285714286 = -2.606898227 Simplifying x + 1.285714286 = -2.606898227 Reorder the terms: 1.285714286 + x = -2.606898227 Solving 1.285714286 + x = -2.606898227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = -2.606898227 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = -2.606898227 + -1.285714286 x = -2.606898227 + -1.285714286 Combine like terms: -2.606898227 + -1.285714286 = -3.892612513 x = -3.892612513 Simplifying x = -3.892612513Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.321183941, -3.892612513}
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