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Simplifying 7x2 + 57x + 42 = 7 Reorder the terms: 42 + 57x + 7x2 = 7 Solving 42 + 57x + 7x2 = 7 Solving for variable 'x'. Reorder the terms: 42 + -7 + 57x + 7x2 = 7 + -7 Combine like terms: 42 + -7 = 35 35 + 57x + 7x2 = 7 + -7 Combine like terms: 7 + -7 = 0 35 + 57x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 5 + 8.142857143x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 8.142857143x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 8.142857143x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8.142857143x + x2 = 0 + -5 8.142857143x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 8.142857143x + x2 = -5 The x term is 8.142857143x. Take half its coefficient (4.071428572). Square it (16.57653062) and add it to both sides. Add '16.57653062' to each side of the equation. 8.142857143x + 16.57653062 + x2 = -5 + 16.57653062 Reorder the terms: 16.57653062 + 8.142857143x + x2 = -5 + 16.57653062 Combine like terms: -5 + 16.57653062 = 11.57653062 16.57653062 + 8.142857143x + x2 = 11.57653062 Factor a perfect square on the left side: (x + 4.071428572)(x + 4.071428572) = 11.57653062 Calculate the square root of the right side: 3.402430105 Break this problem into two subproblems by setting (x + 4.071428572) equal to 3.402430105 and -3.402430105.Subproblem 1
x + 4.071428572 = 3.402430105 Simplifying x + 4.071428572 = 3.402430105 Reorder the terms: 4.071428572 + x = 3.402430105 Solving 4.071428572 + x = 3.402430105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.071428572' to each side of the equation. 4.071428572 + -4.071428572 + x = 3.402430105 + -4.071428572 Combine like terms: 4.071428572 + -4.071428572 = 0.000000000 0.000000000 + x = 3.402430105 + -4.071428572 x = 3.402430105 + -4.071428572 Combine like terms: 3.402430105 + -4.071428572 = -0.668998467 x = -0.668998467 Simplifying x = -0.668998467Subproblem 2
x + 4.071428572 = -3.402430105 Simplifying x + 4.071428572 = -3.402430105 Reorder the terms: 4.071428572 + x = -3.402430105 Solving 4.071428572 + x = -3.402430105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.071428572' to each side of the equation. 4.071428572 + -4.071428572 + x = -3.402430105 + -4.071428572 Combine like terms: 4.071428572 + -4.071428572 = 0.000000000 0.000000000 + x = -3.402430105 + -4.071428572 x = -3.402430105 + -4.071428572 Combine like terms: -3.402430105 + -4.071428572 = -7.473858677 x = -7.473858677 Simplifying x = -7.473858677Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.668998467, -7.473858677}
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