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Simplifying 7x2 + -38x = 15 Reorder the terms: -38x + 7x2 = 15 Solving -38x + 7x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -38x + 7x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -38x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.142857143 + -5.428571429x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + -5.428571429x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + -5.428571429x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + -5.428571429x + x2 = 0 + 2.142857143 -5.428571429x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 -5.428571429x + x2 = 2.142857143 The x term is -5.428571429x. Take half its coefficient (-2.714285715). Square it (7.367346943) and add it to both sides. Add '7.367346943' to each side of the equation. -5.428571429x + 7.367346943 + x2 = 2.142857143 + 7.367346943 Reorder the terms: 7.367346943 + -5.428571429x + x2 = 2.142857143 + 7.367346943 Combine like terms: 2.142857143 + 7.367346943 = 9.510204086 7.367346943 + -5.428571429x + x2 = 9.510204086 Factor a perfect square on the left side: (x + -2.714285715)(x + -2.714285715) = 9.510204086 Calculate the square root of the right side: 3.083861879 Break this problem into two subproblems by setting (x + -2.714285715) equal to 3.083861879 and -3.083861879.Subproblem 1
x + -2.714285715 = 3.083861879 Simplifying x + -2.714285715 = 3.083861879 Reorder the terms: -2.714285715 + x = 3.083861879 Solving -2.714285715 + x = 3.083861879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.714285715' to each side of the equation. -2.714285715 + 2.714285715 + x = 3.083861879 + 2.714285715 Combine like terms: -2.714285715 + 2.714285715 = 0.000000000 0.000000000 + x = 3.083861879 + 2.714285715 x = 3.083861879 + 2.714285715 Combine like terms: 3.083861879 + 2.714285715 = 5.798147594 x = 5.798147594 Simplifying x = 5.798147594Subproblem 2
x + -2.714285715 = -3.083861879 Simplifying x + -2.714285715 = -3.083861879 Reorder the terms: -2.714285715 + x = -3.083861879 Solving -2.714285715 + x = -3.083861879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.714285715' to each side of the equation. -2.714285715 + 2.714285715 + x = -3.083861879 + 2.714285715 Combine like terms: -2.714285715 + 2.714285715 = 0.000000000 0.000000000 + x = -3.083861879 + 2.714285715 x = -3.083861879 + 2.714285715 Combine like terms: -3.083861879 + 2.714285715 = -0.369576164 x = -0.369576164 Simplifying x = -0.369576164Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.798147594, -0.369576164}
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