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Simplifying 0 = 2.2x2 + 6x + -216 Reorder the terms: 0 = -216 + 6x + 2.2x2 Solving 0 = -216 + 6x + 2.2x2 Solving for variable 'x'. Combine like terms: 0 + 216 = 216 216 + -6x + -2.2x2 = -216 + 6x + 2.2x2 + 216 + -6x + -2.2x2 Reorder the terms: 216 + -6x + -2.2x2 = -216 + 216 + 6x + -6x + 2.2x2 + -2.2x2 Combine like terms: -216 + 216 = 0 216 + -6x + -2.2x2 = 0 + 6x + -6x + 2.2x2 + -2.2x2 216 + -6x + -2.2x2 = 6x + -6x + 2.2x2 + -2.2x2 Combine like terms: 6x + -6x = 0 216 + -6x + -2.2x2 = 0 + 2.2x2 + -2.2x2 216 + -6x + -2.2x2 = 2.2x2 + -2.2x2 Combine like terms: 2.2x2 + -2.2x2 = 0.0 216 + -6x + -2.2x2 = 0.0 Begin completing the square. Divide all terms by -2.2 the coefficient of the squared term: Divide each side by '-2.2'. -98.18181818 + 2.727272727x + x2 = 0 Move the constant term to the right: Add '98.18181818' to each side of the equation. -98.18181818 + 2.727272727x + 98.18181818 + x2 = 0 + 98.18181818 Reorder the terms: -98.18181818 + 98.18181818 + 2.727272727x + x2 = 0 + 98.18181818 Combine like terms: -98.18181818 + 98.18181818 = 0.00000000 0.00000000 + 2.727272727x + x2 = 0 + 98.18181818 2.727272727x + x2 = 0 + 98.18181818 Combine like terms: 0 + 98.18181818 = 98.18181818 2.727272727x + x2 = 98.18181818 The x term is 2.727272727x. Take half its coefficient (1.363636364). Square it (1.859504133) and add it to both sides. Add '1.859504133' to each side of the equation. 2.727272727x + 1.859504133 + x2 = 98.18181818 + 1.859504133 Reorder the terms: 1.859504133 + 2.727272727x + x2 = 98.18181818 + 1.859504133 Combine like terms: 98.18181818 + 1.859504133 = 100.041322313 1.859504133 + 2.727272727x + x2 = 100.041322313 Factor a perfect square on the left side: (x + 1.363636364)(x + 1.363636364) = 100.041322313 Calculate the square root of the right side: 10.002065902 Break this problem into two subproblems by setting (x + 1.363636364) equal to 10.002065902 and -10.002065902.Subproblem 1
x + 1.363636364 = 10.002065902 Simplifying x + 1.363636364 = 10.002065902 Reorder the terms: 1.363636364 + x = 10.002065902 Solving 1.363636364 + x = 10.002065902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.363636364' to each side of the equation. 1.363636364 + -1.363636364 + x = 10.002065902 + -1.363636364 Combine like terms: 1.363636364 + -1.363636364 = 0.000000000 0.000000000 + x = 10.002065902 + -1.363636364 x = 10.002065902 + -1.363636364 Combine like terms: 10.002065902 + -1.363636364 = 8.638429538 x = 8.638429538 Simplifying x = 8.638429538Subproblem 2
x + 1.363636364 = -10.002065902 Simplifying x + 1.363636364 = -10.002065902 Reorder the terms: 1.363636364 + x = -10.002065902 Solving 1.363636364 + x = -10.002065902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.363636364' to each side of the equation. 1.363636364 + -1.363636364 + x = -10.002065902 + -1.363636364 Combine like terms: 1.363636364 + -1.363636364 = 0.000000000 0.000000000 + x = -10.002065902 + -1.363636364 x = -10.002065902 + -1.363636364 Combine like terms: -10.002065902 + -1.363636364 = -11.365702266 x = -11.365702266 Simplifying x = -11.365702266Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.638429538, -11.365702266}
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