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Simplifying 7x2 + 142x + -15 = 0 Reorder the terms: -15 + 142x + 7x2 = 0 Solving -15 + 142x + 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'. -2.142857143 + 20.28571429x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + 20.28571429x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + 20.28571429x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + 20.28571429x + x2 = 0 + 2.142857143 20.28571429x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 20.28571429x + x2 = 2.142857143 The x term is 20.28571429x. Take half its coefficient (10.14285715). Square it (102.8775512) and add it to both sides. Add '102.8775512' to each side of the equation. 20.28571429x + 102.8775512 + x2 = 2.142857143 + 102.8775512 Reorder the terms: 102.8775512 + 20.28571429x + x2 = 2.142857143 + 102.8775512 Combine like terms: 2.142857143 + 102.8775512 = 105.020408343 102.8775512 + 20.28571429x + x2 = 105.020408343 Factor a perfect square on the left side: (x + 10.14285715)(x + 10.14285715) = 105.020408343 Calculate the square root of the right side: 10.247946543 Break this problem into two subproblems by setting (x + 10.14285715) equal to 10.247946543 and -10.247946543.Subproblem 1
x + 10.14285715 = 10.247946543 Simplifying x + 10.14285715 = 10.247946543 Reorder the terms: 10.14285715 + x = 10.247946543 Solving 10.14285715 + x = 10.247946543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.14285715' to each side of the equation. 10.14285715 + -10.14285715 + x = 10.247946543 + -10.14285715 Combine like terms: 10.14285715 + -10.14285715 = 0.00000000 0.00000000 + x = 10.247946543 + -10.14285715 x = 10.247946543 + -10.14285715 Combine like terms: 10.247946543 + -10.14285715 = 0.105089393 x = 0.105089393 Simplifying x = 0.105089393Subproblem 2
x + 10.14285715 = -10.247946543 Simplifying x + 10.14285715 = -10.247946543 Reorder the terms: 10.14285715 + x = -10.247946543 Solving 10.14285715 + x = -10.247946543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.14285715' to each side of the equation. 10.14285715 + -10.14285715 + x = -10.247946543 + -10.14285715 Combine like terms: 10.14285715 + -10.14285715 = 0.00000000 0.00000000 + x = -10.247946543 + -10.14285715 x = -10.247946543 + -10.14285715 Combine like terms: -10.247946543 + -10.14285715 = -20.390803693 x = -20.390803693 Simplifying x = -20.390803693Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.105089393, -20.390803693}
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