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Simplifying 7x2 + -26x + 8 = 0 Reorder the terms: 8 + -26x + 7x2 = 0 Solving 8 + -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'. 1.142857143 + -3.714285714x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + -3.714285714x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + -3.714285714x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + -3.714285714x + x2 = 0 + -1.142857143 -3.714285714x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 -3.714285714x + x2 = -1.142857143 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 = -1.142857143 + 3.448979591 Reorder the terms: 3.448979591 + -3.714285714x + x2 = -1.142857143 + 3.448979591 Combine like terms: -1.142857143 + 3.448979591 = 2.306122448 3.448979591 + -3.714285714x + x2 = 2.306122448 Factor a perfect square on the left side: (x + -1.857142857)(x + -1.857142857) = 2.306122448 Calculate the square root of the right side: 1.518592259 Break this problem into two subproblems by setting (x + -1.857142857) equal to 1.518592259 and -1.518592259.Subproblem 1
x + -1.857142857 = 1.518592259 Simplifying x + -1.857142857 = 1.518592259 Reorder the terms: -1.857142857 + x = 1.518592259 Solving -1.857142857 + x = 1.518592259 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 = 1.518592259 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = 1.518592259 + 1.857142857 x = 1.518592259 + 1.857142857 Combine like terms: 1.518592259 + 1.857142857 = 3.375735116 x = 3.375735116 Simplifying x = 3.375735116Subproblem 2
x + -1.857142857 = -1.518592259 Simplifying x + -1.857142857 = -1.518592259 Reorder the terms: -1.857142857 + x = -1.518592259 Solving -1.857142857 + x = -1.518592259 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 = -1.518592259 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = -1.518592259 + 1.857142857 x = -1.518592259 + 1.857142857 Combine like terms: -1.518592259 + 1.857142857 = 0.338550598 x = 0.338550598 Simplifying x = 0.338550598Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.375735116, 0.338550598}
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