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Simplifying 7x2 + -12x + -54 = 0 Reorder the terms: -54 + -12x + 7x2 = 0 Solving -54 + -12x + 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'. -7.714285714 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '7.714285714' to each side of the equation. -7.714285714 + -1.714285714x + 7.714285714 + x2 = 0 + 7.714285714 Reorder the terms: -7.714285714 + 7.714285714 + -1.714285714x + x2 = 0 + 7.714285714 Combine like terms: -7.714285714 + 7.714285714 = 0.000000000 0.000000000 + -1.714285714x + x2 = 0 + 7.714285714 -1.714285714x + x2 = 0 + 7.714285714 Combine like terms: 0 + 7.714285714 = 7.714285714 -1.714285714x + x2 = 7.714285714 The x term is -1.714285714x. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714x + 0.7346938773 + x2 = 7.714285714 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = 7.714285714 + 0.7346938773 Combine like terms: 7.714285714 + 0.7346938773 = 8.4489795913 0.7346938773 + -1.714285714x + x2 = 8.4489795913 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 8.4489795913 Calculate the square root of the right side: 2.90671285 Break this problem into two subproblems by setting (x + -0.857142857) equal to 2.90671285 and -2.90671285.Subproblem 1
x + -0.857142857 = 2.90671285 Simplifying x + -0.857142857 = 2.90671285 Reorder the terms: -0.857142857 + x = 2.90671285 Solving -0.857142857 + x = 2.90671285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 2.90671285 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 2.90671285 + 0.857142857 x = 2.90671285 + 0.857142857 Combine like terms: 2.90671285 + 0.857142857 = 3.763855707 x = 3.763855707 Simplifying x = 3.763855707Subproblem 2
x + -0.857142857 = -2.90671285 Simplifying x + -0.857142857 = -2.90671285 Reorder the terms: -0.857142857 + x = -2.90671285 Solving -0.857142857 + x = -2.90671285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -2.90671285 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -2.90671285 + 0.857142857 x = -2.90671285 + 0.857142857 Combine like terms: -2.90671285 + 0.857142857 = -2.049569993 x = -2.049569993 Simplifying x = -2.049569993Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.763855707, -2.049569993}
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