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Simplifying 7x(x + -11) + -3x = -53 Reorder the terms: 7x(-11 + x) + -3x = -53 (-11 * 7x + x * 7x) + -3x = -53 (-77x + 7x2) + -3x = -53 Reorder the terms: -77x + -3x + 7x2 = -53 Combine like terms: -77x + -3x = -80x -80x + 7x2 = -53 Solving -80x + 7x2 = -53 Solving for variable 'x'. Reorder the terms: 53 + -80x + 7x2 = -53 + 53 Combine like terms: -53 + 53 = 0 53 + -80x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 7.571428571 + -11.42857143x + x2 = 0 Move the constant term to the right: Add '-7.571428571' to each side of the equation. 7.571428571 + -11.42857143x + -7.571428571 + x2 = 0 + -7.571428571 Reorder the terms: 7.571428571 + -7.571428571 + -11.42857143x + x2 = 0 + -7.571428571 Combine like terms: 7.571428571 + -7.571428571 = 0.000000000 0.000000000 + -11.42857143x + x2 = 0 + -7.571428571 -11.42857143x + x2 = 0 + -7.571428571 Combine like terms: 0 + -7.571428571 = -7.571428571 -11.42857143x + x2 = -7.571428571 The x term is -11.42857143x. Take half its coefficient (-5.714285715). Square it (32.65306123) and add it to both sides. Add '32.65306123' to each side of the equation. -11.42857143x + 32.65306123 + x2 = -7.571428571 + 32.65306123 Reorder the terms: 32.65306123 + -11.42857143x + x2 = -7.571428571 + 32.65306123 Combine like terms: -7.571428571 + 32.65306123 = 25.081632659 32.65306123 + -11.42857143x + x2 = 25.081632659 Factor a perfect square on the left side: (x + -5.714285715)(x + -5.714285715) = 25.081632659 Calculate the square root of the right side: 5.008156613 Break this problem into two subproblems by setting (x + -5.714285715) equal to 5.008156613 and -5.008156613.Subproblem 1
x + -5.714285715 = 5.008156613 Simplifying x + -5.714285715 = 5.008156613 Reorder the terms: -5.714285715 + x = 5.008156613 Solving -5.714285715 + x = 5.008156613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.714285715' to each side of the equation. -5.714285715 + 5.714285715 + x = 5.008156613 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = 5.008156613 + 5.714285715 x = 5.008156613 + 5.714285715 Combine like terms: 5.008156613 + 5.714285715 = 10.722442328 x = 10.722442328 Simplifying x = 10.722442328Subproblem 2
x + -5.714285715 = -5.008156613 Simplifying x + -5.714285715 = -5.008156613 Reorder the terms: -5.714285715 + x = -5.008156613 Solving -5.714285715 + x = -5.008156613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.714285715' to each side of the equation. -5.714285715 + 5.714285715 + x = -5.008156613 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = -5.008156613 + 5.714285715 x = -5.008156613 + 5.714285715 Combine like terms: -5.008156613 + 5.714285715 = 0.706129102 x = 0.706129102 Simplifying x = 0.706129102Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.722442328, 0.706129102}
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