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Simplifying 7x2 + -30x + -27 = 0 Reorder the terms: -27 + -30x + 7x2 = 0 Solving -27 + -30x + 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'. -3.857142857 + -4.285714286x + x2 = 0 Move the constant term to the right: Add '3.857142857' to each side of the equation. -3.857142857 + -4.285714286x + 3.857142857 + x2 = 0 + 3.857142857 Reorder the terms: -3.857142857 + 3.857142857 + -4.285714286x + x2 = 0 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + -4.285714286x + x2 = 0 + 3.857142857 -4.285714286x + x2 = 0 + 3.857142857 Combine like terms: 0 + 3.857142857 = 3.857142857 -4.285714286x + x2 = 3.857142857 The x term is -4.285714286x. Take half its coefficient (-2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. -4.285714286x + 4.591836735 + x2 = 3.857142857 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286x + x2 = 3.857142857 + 4.591836735 Combine like terms: 3.857142857 + 4.591836735 = 8.448979592 4.591836735 + -4.285714286x + x2 = 8.448979592 Factor a perfect square on the left side: (x + -2.142857143)(x + -2.142857143) = 8.448979592 Calculate the square root of the right side: 2.90671285 Break this problem into two subproblems by setting (x + -2.142857143) equal to 2.90671285 and -2.90671285.Subproblem 1
x + -2.142857143 = 2.90671285 Simplifying x + -2.142857143 = 2.90671285 Reorder the terms: -2.142857143 + x = 2.90671285 Solving -2.142857143 + x = 2.90671285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + x = 2.90671285 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = 2.90671285 + 2.142857143 x = 2.90671285 + 2.142857143 Combine like terms: 2.90671285 + 2.142857143 = 5.049569993 x = 5.049569993 Simplifying x = 5.049569993Subproblem 2
x + -2.142857143 = -2.90671285 Simplifying x + -2.142857143 = -2.90671285 Reorder the terms: -2.142857143 + x = -2.90671285 Solving -2.142857143 + x = -2.90671285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + x = -2.90671285 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = -2.90671285 + 2.142857143 x = -2.90671285 + 2.142857143 Combine like terms: -2.90671285 + 2.142857143 = -0.763855707 x = -0.763855707 Simplifying x = -0.763855707Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.049569993, -0.763855707}
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