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Simplifying 7x2 + -22x + -8 = 0 Reorder the terms: -8 + -22x + 7x2 = 0 Solving -8 + -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'. -1.142857143 + -3.142857143x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -3.142857143x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -3.142857143x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -3.142857143x + x2 = 0 + 1.142857143 -3.142857143x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -3.142857143x + x2 = 1.142857143 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 = 1.142857143 + 2.469387757 Reorder the terms: 2.469387757 + -3.142857143x + x2 = 1.142857143 + 2.469387757 Combine like terms: 1.142857143 + 2.469387757 = 3.6122449 2.469387757 + -3.142857143x + x2 = 3.6122449 Factor a perfect square on the left side: (x + -1.571428572)(x + -1.571428572) = 3.6122449 Calculate the square root of the right side: 1.900590671 Break this problem into two subproblems by setting (x + -1.571428572) equal to 1.900590671 and -1.900590671.Subproblem 1
x + -1.571428572 = 1.900590671 Simplifying x + -1.571428572 = 1.900590671 Reorder the terms: -1.571428572 + x = 1.900590671 Solving -1.571428572 + x = 1.900590671 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 = 1.900590671 + 1.571428572 Combine like terms: -1.571428572 + 1.571428572 = 0.000000000 0.000000000 + x = 1.900590671 + 1.571428572 x = 1.900590671 + 1.571428572 Combine like terms: 1.900590671 + 1.571428572 = 3.472019243 x = 3.472019243 Simplifying x = 3.472019243Subproblem 2
x + -1.571428572 = -1.900590671 Simplifying x + -1.571428572 = -1.900590671 Reorder the terms: -1.571428572 + x = -1.900590671 Solving -1.571428572 + x = -1.900590671 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 = -1.900590671 + 1.571428572 Combine like terms: -1.571428572 + 1.571428572 = 0.000000000 0.000000000 + x = -1.900590671 + 1.571428572 x = -1.900590671 + 1.571428572 Combine like terms: -1.900590671 + 1.571428572 = -0.329162099 x = -0.329162099 Simplifying x = -0.329162099Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.472019243, -0.329162099}
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