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Simplifying 7x2 = -226x + 528 Reorder the terms: 7x2 = 528 + -226x Solving 7x2 = 528 + -226x Solving for variable 'x'. Reorder the terms: -528 + 226x + 7x2 = 528 + -226x + -528 + 226x Reorder the terms: -528 + 226x + 7x2 = 528 + -528 + -226x + 226x Combine like terms: 528 + -528 = 0 -528 + 226x + 7x2 = 0 + -226x + 226x -528 + 226x + 7x2 = -226x + 226x Combine like terms: -226x + 226x = 0 -528 + 226x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -75.42857143 + 32.28571429x + x2 = 0 Move the constant term to the right: Add '75.42857143' to each side of the equation. -75.42857143 + 32.28571429x + 75.42857143 + x2 = 0 + 75.42857143 Reorder the terms: -75.42857143 + 75.42857143 + 32.28571429x + x2 = 0 + 75.42857143 Combine like terms: -75.42857143 + 75.42857143 = 0.00000000 0.00000000 + 32.28571429x + x2 = 0 + 75.42857143 32.28571429x + x2 = 0 + 75.42857143 Combine like terms: 0 + 75.42857143 = 75.42857143 32.28571429x + x2 = 75.42857143 The x term is 32.28571429x. Take half its coefficient (16.14285715). Square it (260.5918370) and add it to both sides. Add '260.5918370' to each side of the equation. 32.28571429x + 260.5918370 + x2 = 75.42857143 + 260.5918370 Reorder the terms: 260.5918370 + 32.28571429x + x2 = 75.42857143 + 260.5918370 Combine like terms: 75.42857143 + 260.5918370 = 336.02040843 260.5918370 + 32.28571429x + x2 = 336.02040843 Factor a perfect square on the left side: (x + 16.14285715)(x + 16.14285715) = 336.02040843 Calculate the square root of the right side: 18.330859457 Break this problem into two subproblems by setting (x + 16.14285715) equal to 18.330859457 and -18.330859457.Subproblem 1
x + 16.14285715 = 18.330859457 Simplifying x + 16.14285715 = 18.330859457 Reorder the terms: 16.14285715 + x = 18.330859457 Solving 16.14285715 + x = 18.330859457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.14285715' to each side of the equation. 16.14285715 + -16.14285715 + x = 18.330859457 + -16.14285715 Combine like terms: 16.14285715 + -16.14285715 = 0.00000000 0.00000000 + x = 18.330859457 + -16.14285715 x = 18.330859457 + -16.14285715 Combine like terms: 18.330859457 + -16.14285715 = 2.188002307 x = 2.188002307 Simplifying x = 2.188002307Subproblem 2
x + 16.14285715 = -18.330859457 Simplifying x + 16.14285715 = -18.330859457 Reorder the terms: 16.14285715 + x = -18.330859457 Solving 16.14285715 + x = -18.330859457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.14285715' to each side of the equation. 16.14285715 + -16.14285715 + x = -18.330859457 + -16.14285715 Combine like terms: 16.14285715 + -16.14285715 = 0.00000000 0.00000000 + x = -18.330859457 + -16.14285715 x = -18.330859457 + -16.14285715 Combine like terms: -18.330859457 + -16.14285715 = -34.473716607 x = -34.473716607 Simplifying x = -34.473716607Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.188002307, -34.473716607}
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