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Simplifying 14x2 + 9x + -3 = 0 Reorder the terms: -3 + 9x + 14x2 = 0 Solving -3 + 9x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2142857143 + 0.6428571429x + x2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.6428571429x + 0.2142857143 + x2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + 0.6428571429x + x2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + 0.6428571429x + x2 = 0 + 0.2142857143 0.6428571429x + x2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 0.6428571429x + x2 = 0.2142857143 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 = 0.2142857143 + 0.1033163266 Reorder the terms: 0.1033163266 + 0.6428571429x + x2 = 0.2142857143 + 0.1033163266 Combine like terms: 0.2142857143 + 0.1033163266 = 0.3176020409 0.1033163266 + 0.6428571429x + x2 = 0.3176020409 Factor a perfect square on the left side: (x + 0.3214285715)(x + 0.3214285715) = 0.3176020409 Calculate the square root of the right side: 0.563561923 Break this problem into two subproblems by setting (x + 0.3214285715) equal to 0.563561923 and -0.563561923.Subproblem 1
x + 0.3214285715 = 0.563561923 Simplifying x + 0.3214285715 = 0.563561923 Reorder the terms: 0.3214285715 + x = 0.563561923 Solving 0.3214285715 + x = 0.563561923 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 = 0.563561923 + -0.3214285715 Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000 0.0000000000 + x = 0.563561923 + -0.3214285715 x = 0.563561923 + -0.3214285715 Combine like terms: 0.563561923 + -0.3214285715 = 0.2421333515 x = 0.2421333515 Simplifying x = 0.2421333515Subproblem 2
x + 0.3214285715 = -0.563561923 Simplifying x + 0.3214285715 = -0.563561923 Reorder the terms: 0.3214285715 + x = -0.563561923 Solving 0.3214285715 + x = -0.563561923 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 = -0.563561923 + -0.3214285715 Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000 0.0000000000 + x = -0.563561923 + -0.3214285715 x = -0.563561923 + -0.3214285715 Combine like terms: -0.563561923 + -0.3214285715 = -0.8849904945 x = -0.8849904945 Simplifying x = -0.8849904945Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2421333515, -0.8849904945}
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