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Simplifying 8.8x2 + 2.1x + -9.2 = 0 Reorder the terms: -9.2 + 2.1x + 8.8x2 = 0 Solving -9.2 + 2.1x + 8.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8.8 the coefficient of the squared term: Divide each side by '8.8'. -1.045454545 + 0.2386363636x + x2 = 0 Move the constant term to the right: Add '1.045454545' to each side of the equation. -1.045454545 + 0.2386363636x + 1.045454545 + x2 = 0 + 1.045454545 Reorder the terms: -1.045454545 + 1.045454545 + 0.2386363636x + x2 = 0 + 1.045454545 Combine like terms: -1.045454545 + 1.045454545 = 0.000000000 0.000000000 + 0.2386363636x + x2 = 0 + 1.045454545 0.2386363636x + x2 = 0 + 1.045454545 Combine like terms: 0 + 1.045454545 = 1.045454545 0.2386363636x + x2 = 1.045454545 The x term is 0.2386363636x. Take half its coefficient (0.1193181818). Square it (0.01423682851) and add it to both sides. Add '0.01423682851' to each side of the equation. 0.2386363636x + 0.01423682851 + x2 = 1.045454545 + 0.01423682851 Reorder the terms: 0.01423682851 + 0.2386363636x + x2 = 1.045454545 + 0.01423682851 Combine like terms: 1.045454545 + 0.01423682851 = 1.05969137351 0.01423682851 + 0.2386363636x + x2 = 1.05969137351 Factor a perfect square on the left side: (x + 0.1193181818)(x + 0.1193181818) = 1.05969137351 Calculate the square root of the right side: 1.029413121 Break this problem into two subproblems by setting (x + 0.1193181818) equal to 1.029413121 and -1.029413121.Subproblem 1
x + 0.1193181818 = 1.029413121 Simplifying x + 0.1193181818 = 1.029413121 Reorder the terms: 0.1193181818 + x = 1.029413121 Solving 0.1193181818 + x = 1.029413121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1193181818' to each side of the equation. 0.1193181818 + -0.1193181818 + x = 1.029413121 + -0.1193181818 Combine like terms: 0.1193181818 + -0.1193181818 = 0.0000000000 0.0000000000 + x = 1.029413121 + -0.1193181818 x = 1.029413121 + -0.1193181818 Combine like terms: 1.029413121 + -0.1193181818 = 0.9100949392 x = 0.9100949392 Simplifying x = 0.9100949392Subproblem 2
x + 0.1193181818 = -1.029413121 Simplifying x + 0.1193181818 = -1.029413121 Reorder the terms: 0.1193181818 + x = -1.029413121 Solving 0.1193181818 + x = -1.029413121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1193181818' to each side of the equation. 0.1193181818 + -0.1193181818 + x = -1.029413121 + -0.1193181818 Combine like terms: 0.1193181818 + -0.1193181818 = 0.0000000000 0.0000000000 + x = -1.029413121 + -0.1193181818 x = -1.029413121 + -0.1193181818 Combine like terms: -1.029413121 + -0.1193181818 = -1.1487313028 x = -1.1487313028 Simplifying x = -1.1487313028Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9100949392, -1.1487313028}
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