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Simplifying (19 + -1x2) = 4(22 + 20x + -2x2) Remove parenthesis around (19 + -1x2) 19 + -1x2 = 4(22 + 20x + -2x2) 19 + -1x2 = (22 * 4 + 20x * 4 + -2x2 * 4) 19 + -1x2 = (88 + 80x + -8x2) Solving 19 + -1x2 = 88 + 80x + -8x2 Solving for variable 'x'. Reorder the terms: 19 + -88 + -80x + -1x2 + 8x2 = 88 + 80x + -8x2 + -88 + -80x + 8x2 Combine like terms: 19 + -88 = -69 -69 + -80x + -1x2 + 8x2 = 88 + 80x + -8x2 + -88 + -80x + 8x2 Combine like terms: -1x2 + 8x2 = 7x2 -69 + -80x + 7x2 = 88 + 80x + -8x2 + -88 + -80x + 8x2 Reorder the terms: -69 + -80x + 7x2 = 88 + -88 + 80x + -80x + -8x2 + 8x2 Combine like terms: 88 + -88 = 0 -69 + -80x + 7x2 = 0 + 80x + -80x + -8x2 + 8x2 -69 + -80x + 7x2 = 80x + -80x + -8x2 + 8x2 Combine like terms: 80x + -80x = 0 -69 + -80x + 7x2 = 0 + -8x2 + 8x2 -69 + -80x + 7x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -69 + -80x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -9.857142857 + -11.42857143x + x2 = 0 Move the constant term to the right: Add '9.857142857' to each side of the equation. -9.857142857 + -11.42857143x + 9.857142857 + x2 = 0 + 9.857142857 Reorder the terms: -9.857142857 + 9.857142857 + -11.42857143x + x2 = 0 + 9.857142857 Combine like terms: -9.857142857 + 9.857142857 = 0.000000000 0.000000000 + -11.42857143x + x2 = 0 + 9.857142857 -11.42857143x + x2 = 0 + 9.857142857 Combine like terms: 0 + 9.857142857 = 9.857142857 -11.42857143x + x2 = 9.857142857 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 = 9.857142857 + 32.65306123 Reorder the terms: 32.65306123 + -11.42857143x + x2 = 9.857142857 + 32.65306123 Combine like terms: 9.857142857 + 32.65306123 = 42.510204087 32.65306123 + -11.42857143x + x2 = 42.510204087 Factor a perfect square on the left side: (x + -5.714285715)(x + -5.714285715) = 42.510204087 Calculate the square root of the right side: 6.519984976 Break this problem into two subproblems by setting (x + -5.714285715) equal to 6.519984976 and -6.519984976.Subproblem 1
x + -5.714285715 = 6.519984976 Simplifying x + -5.714285715 = 6.519984976 Reorder the terms: -5.714285715 + x = 6.519984976 Solving -5.714285715 + x = 6.519984976 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 = 6.519984976 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = 6.519984976 + 5.714285715 x = 6.519984976 + 5.714285715 Combine like terms: 6.519984976 + 5.714285715 = 12.234270691 x = 12.234270691 Simplifying x = 12.234270691Subproblem 2
x + -5.714285715 = -6.519984976 Simplifying x + -5.714285715 = -6.519984976 Reorder the terms: -5.714285715 + x = -6.519984976 Solving -5.714285715 + x = -6.519984976 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 = -6.519984976 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = -6.519984976 + 5.714285715 x = -6.519984976 + 5.714285715 Combine like terms: -6.519984976 + 5.714285715 = -0.805699261 x = -0.805699261 Simplifying x = -0.805699261Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.234270691, -0.805699261}
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