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Simplifying 1.4x2 + 0.9x + -31.7 = 0 Reorder the terms: -31.7 + 0.9x + 1.4x2 = 0 Solving -31.7 + 0.9x + 1.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. -22.64285714 + 0.6428571429x + x2 = 0 Move the constant term to the right: Add '22.64285714' to each side of the equation. -22.64285714 + 0.6428571429x + 22.64285714 + x2 = 0 + 22.64285714 Reorder the terms: -22.64285714 + 22.64285714 + 0.6428571429x + x2 = 0 + 22.64285714 Combine like terms: -22.64285714 + 22.64285714 = 0.00000000 0.00000000 + 0.6428571429x + x2 = 0 + 22.64285714 0.6428571429x + x2 = 0 + 22.64285714 Combine like terms: 0 + 22.64285714 = 22.64285714 0.6428571429x + x2 = 22.64285714 The x term is 0.6428571429x. Take half its coefficient (0.3214285715). Square it (0.1033163266) and add it to both sides. Add '0.1033163266' to each side of the equation. 0.6428571429x + 0.1033163266 + x2 = 22.64285714 + 0.1033163266 Reorder the terms: 0.1033163266 + 0.6428571429x + x2 = 22.64285714 + 0.1033163266 Combine like terms: 22.64285714 + 0.1033163266 = 22.7461734666 0.1033163266 + 0.6428571429x + x2 = 22.7461734666 Factor a perfect square on the left side: (x + 0.3214285715)(x + 0.3214285715) = 22.7461734666 Calculate the square root of the right side: 4.769294861 Break this problem into two subproblems by setting (x + 0.3214285715) equal to 4.769294861 and -4.769294861.Subproblem 1
x + 0.3214285715 = 4.769294861 Simplifying x + 0.3214285715 = 4.769294861 Reorder the terms: 0.3214285715 + x = 4.769294861 Solving 0.3214285715 + x = 4.769294861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3214285715' to each side of the equation. 0.3214285715 + -0.3214285715 + x = 4.769294861 + -0.3214285715 Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000 0.0000000000 + x = 4.769294861 + -0.3214285715 x = 4.769294861 + -0.3214285715 Combine like terms: 4.769294861 + -0.3214285715 = 4.4478662895 x = 4.4478662895 Simplifying x = 4.4478662895Subproblem 2
x + 0.3214285715 = -4.769294861 Simplifying x + 0.3214285715 = -4.769294861 Reorder the terms: 0.3214285715 + x = -4.769294861 Solving 0.3214285715 + x = -4.769294861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3214285715' to each side of the equation. 0.3214285715 + -0.3214285715 + x = -4.769294861 + -0.3214285715 Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000 0.0000000000 + x = -4.769294861 + -0.3214285715 x = -4.769294861 + -0.3214285715 Combine like terms: -4.769294861 + -0.3214285715 = -5.0907234325 x = -5.0907234325 Simplifying x = -5.0907234325Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4478662895, -5.0907234325}
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