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Simplifying 16x2 + -80x + -100 + -1(9x2 + 6x + 1) = 0 Reorder the terms: 16x2 + -80x + -100 + -1(1 + 6x + 9x2) = 0 16x2 + -80x + -100 + (1 * -1 + 6x * -1 + 9x2 * -1) = 0 16x2 + -80x + -100 + (-1 + -6x + -9x2) = 0 Reorder the terms: -100 + -1 + -80x + -6x + 16x2 + -9x2 = 0 Combine like terms: -100 + -1 = -101 -101 + -80x + -6x + 16x2 + -9x2 = 0 Combine like terms: -80x + -6x = -86x -101 + -86x + 16x2 + -9x2 = 0 Combine like terms: 16x2 + -9x2 = 7x2 -101 + -86x + 7x2 = 0 Solving -101 + -86x + 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'. -14.42857143 + -12.28571429x + x2 = 0 Move the constant term to the right: Add '14.42857143' to each side of the equation. -14.42857143 + -12.28571429x + 14.42857143 + x2 = 0 + 14.42857143 Reorder the terms: -14.42857143 + 14.42857143 + -12.28571429x + x2 = 0 + 14.42857143 Combine like terms: -14.42857143 + 14.42857143 = 0.00000000 0.00000000 + -12.28571429x + x2 = 0 + 14.42857143 -12.28571429x + x2 = 0 + 14.42857143 Combine like terms: 0 + 14.42857143 = 14.42857143 -12.28571429x + x2 = 14.42857143 The x term is -12.28571429x. Take half its coefficient (-6.142857145). Square it (37.73469390) and add it to both sides. Add '37.73469390' to each side of the equation. -12.28571429x + 37.73469390 + x2 = 14.42857143 + 37.73469390 Reorder the terms: 37.73469390 + -12.28571429x + x2 = 14.42857143 + 37.73469390 Combine like terms: 14.42857143 + 37.73469390 = 52.16326533 37.73469390 + -12.28571429x + x2 = 52.16326533 Factor a perfect square on the left side: (x + -6.142857145)(x + -6.142857145) = 52.16326533 Calculate the square root of the right side: 7.222414093 Break this problem into two subproblems by setting (x + -6.142857145) equal to 7.222414093 and -7.222414093.Subproblem 1
x + -6.142857145 = 7.222414093 Simplifying x + -6.142857145 = 7.222414093 Reorder the terms: -6.142857145 + x = 7.222414093 Solving -6.142857145 + x = 7.222414093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.142857145' to each side of the equation. -6.142857145 + 6.142857145 + x = 7.222414093 + 6.142857145 Combine like terms: -6.142857145 + 6.142857145 = 0.000000000 0.000000000 + x = 7.222414093 + 6.142857145 x = 7.222414093 + 6.142857145 Combine like terms: 7.222414093 + 6.142857145 = 13.365271238 x = 13.365271238 Simplifying x = 13.365271238Subproblem 2
x + -6.142857145 = -7.222414093 Simplifying x + -6.142857145 = -7.222414093 Reorder the terms: -6.142857145 + x = -7.222414093 Solving -6.142857145 + x = -7.222414093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.142857145' to each side of the equation. -6.142857145 + 6.142857145 + x = -7.222414093 + 6.142857145 Combine like terms: -6.142857145 + 6.142857145 = 0.000000000 0.000000000 + x = -7.222414093 + 6.142857145 x = -7.222414093 + 6.142857145 Combine like terms: -7.222414093 + 6.142857145 = -1.079556948 x = -1.079556948 Simplifying x = -1.079556948Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.365271238, -1.079556948}
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