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Simplifying 7x2 + 22x + 2.5 = 0 Reorder the terms: 2.5 + 22x + 7x2 = 0 Solving 2.5 + 22x + 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'. 0.3571428571 + 3.142857143x + x2 = 0 Move the constant term to the right: Add '-0.3571428571' to each side of the equation. 0.3571428571 + 3.142857143x + -0.3571428571 + x2 = 0 + -0.3571428571 Reorder the terms: 0.3571428571 + -0.3571428571 + 3.142857143x + x2 = 0 + -0.3571428571 Combine like terms: 0.3571428571 + -0.3571428571 = 0.0000000000 0.0000000000 + 3.142857143x + x2 = 0 + -0.3571428571 3.142857143x + x2 = 0 + -0.3571428571 Combine like terms: 0 + -0.3571428571 = -0.3571428571 3.142857143x + x2 = -0.3571428571 The x term is 3.142857143x. Take half its coefficient (1.571428572). Square it (2.469387757) and add it to both sides. Add '2.469387757' to each side of the equation. 3.142857143x + 2.469387757 + x2 = -0.3571428571 + 2.469387757 Reorder the terms: 2.469387757 + 3.142857143x + x2 = -0.3571428571 + 2.469387757 Combine like terms: -0.3571428571 + 2.469387757 = 2.1122448999 2.469387757 + 3.142857143x + x2 = 2.1122448999 Factor a perfect square on the left side: (x + 1.571428572)(x + 1.571428572) = 2.1122448999 Calculate the square root of the right side: 1.453356426 Break this problem into two subproblems by setting (x + 1.571428572) equal to 1.453356426 and -1.453356426.Subproblem 1
x + 1.571428572 = 1.453356426 Simplifying x + 1.571428572 = 1.453356426 Reorder the terms: 1.571428572 + x = 1.453356426 Solving 1.571428572 + x = 1.453356426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = 1.453356426 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = 1.453356426 + -1.571428572 x = 1.453356426 + -1.571428572 Combine like terms: 1.453356426 + -1.571428572 = -0.118072146 x = -0.118072146 Simplifying x = -0.118072146Subproblem 2
x + 1.571428572 = -1.453356426 Simplifying x + 1.571428572 = -1.453356426 Reorder the terms: 1.571428572 + x = -1.453356426 Solving 1.571428572 + x = -1.453356426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = -1.453356426 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = -1.453356426 + -1.571428572 x = -1.453356426 + -1.571428572 Combine like terms: -1.453356426 + -1.571428572 = -3.024784998 x = -3.024784998 Simplifying x = -3.024784998Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.118072146, -3.024784998}
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