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Simplifying 7x2 + -4x + -80 = 0 Reorder the terms: -80 + -4x + 7x2 = 0 Solving -80 + -4x + 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'. -11.42857143 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '11.42857143' to each side of the equation. -11.42857143 + -0.5714285714x + 11.42857143 + x2 = 0 + 11.42857143 Reorder the terms: -11.42857143 + 11.42857143 + -0.5714285714x + x2 = 0 + 11.42857143 Combine like terms: -11.42857143 + 11.42857143 = 0.00000000 0.00000000 + -0.5714285714x + x2 = 0 + 11.42857143 -0.5714285714x + x2 = 0 + 11.42857143 Combine like terms: 0 + 11.42857143 = 11.42857143 -0.5714285714x + x2 = 11.42857143 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 11.42857143 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 11.42857143 + 0.08163265305 Combine like terms: 11.42857143 + 0.08163265305 = 11.51020408305 0.08163265305 + -0.5714285714x + x2 = 11.51020408305 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 11.51020408305 Calculate the square root of the right side: 3.392669168 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 3.392669168 and -3.392669168.Subproblem 1
x + -0.2857142857 = 3.392669168 Simplifying x + -0.2857142857 = 3.392669168 Reorder the terms: -0.2857142857 + x = 3.392669168 Solving -0.2857142857 + x = 3.392669168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 3.392669168 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 3.392669168 + 0.2857142857 x = 3.392669168 + 0.2857142857 Combine like terms: 3.392669168 + 0.2857142857 = 3.6783834537 x = 3.6783834537 Simplifying x = 3.6783834537Subproblem 2
x + -0.2857142857 = -3.392669168 Simplifying x + -0.2857142857 = -3.392669168 Reorder the terms: -0.2857142857 + x = -3.392669168 Solving -0.2857142857 + x = -3.392669168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -3.392669168 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -3.392669168 + 0.2857142857 x = -3.392669168 + 0.2857142857 Combine like terms: -3.392669168 + 0.2857142857 = -3.1069548823 x = -3.1069548823 Simplifying x = -3.1069548823Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6783834537, -3.1069548823}
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