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Simplifying 7x2 + -26x + -2 = 0 Reorder the terms: -2 + -26x + 7x2 = 0 Solving -2 + -26x + 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'. -0.2857142857 + -3.714285714x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -3.714285714x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -3.714285714x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -3.714285714x + x2 = 0 + 0.2857142857 -3.714285714x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -3.714285714x + x2 = 0.2857142857 The x term is -3.714285714x. Take half its coefficient (-1.857142857). Square it (3.448979591) and add it to both sides. Add '3.448979591' to each side of the equation. -3.714285714x + 3.448979591 + x2 = 0.2857142857 + 3.448979591 Reorder the terms: 3.448979591 + -3.714285714x + x2 = 0.2857142857 + 3.448979591 Combine like terms: 0.2857142857 + 3.448979591 = 3.7346938767 3.448979591 + -3.714285714x + x2 = 3.7346938767 Factor a perfect square on the left side: (x + -1.857142857)(x + -1.857142857) = 3.7346938767 Calculate the square root of the right side: 1.932535608 Break this problem into two subproblems by setting (x + -1.857142857) equal to 1.932535608 and -1.932535608.Subproblem 1
x + -1.857142857 = 1.932535608 Simplifying x + -1.857142857 = 1.932535608 Reorder the terms: -1.857142857 + x = 1.932535608 Solving -1.857142857 + x = 1.932535608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + x = 1.932535608 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = 1.932535608 + 1.857142857 x = 1.932535608 + 1.857142857 Combine like terms: 1.932535608 + 1.857142857 = 3.789678465 x = 3.789678465 Simplifying x = 3.789678465Subproblem 2
x + -1.857142857 = -1.932535608 Simplifying x + -1.857142857 = -1.932535608 Reorder the terms: -1.857142857 + x = -1.932535608 Solving -1.857142857 + x = -1.932535608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + x = -1.932535608 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = -1.932535608 + 1.857142857 x = -1.932535608 + 1.857142857 Combine like terms: -1.932535608 + 1.857142857 = -0.075392751 x = -0.075392751 Simplifying x = -0.075392751Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.789678465, -0.075392751}
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