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Simplifying 7x2 + -90x + 260 = 0 Reorder the terms: 260 + -90x + 7x2 = 0 Solving 260 + -90x + 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'. 37.14285714 + -12.85714286x + x2 = 0 Move the constant term to the right: Add '-37.14285714' to each side of the equation. 37.14285714 + -12.85714286x + -37.14285714 + x2 = 0 + -37.14285714 Reorder the terms: 37.14285714 + -37.14285714 + -12.85714286x + x2 = 0 + -37.14285714 Combine like terms: 37.14285714 + -37.14285714 = 0.00000000 0.00000000 + -12.85714286x + x2 = 0 + -37.14285714 -12.85714286x + x2 = 0 + -37.14285714 Combine like terms: 0 + -37.14285714 = -37.14285714 -12.85714286x + x2 = -37.14285714 The x term is -12.85714286x. Take half its coefficient (-6.42857143). Square it (41.32653063) and add it to both sides. Add '41.32653063' to each side of the equation. -12.85714286x + 41.32653063 + x2 = -37.14285714 + 41.32653063 Reorder the terms: 41.32653063 + -12.85714286x + x2 = -37.14285714 + 41.32653063 Combine like terms: -37.14285714 + 41.32653063 = 4.18367349 41.32653063 + -12.85714286x + x2 = 4.18367349 Factor a perfect square on the left side: (x + -6.42857143)(x + -6.42857143) = 4.18367349 Calculate the square root of the right side: 2.045403014 Break this problem into two subproblems by setting (x + -6.42857143) equal to 2.045403014 and -2.045403014.Subproblem 1
x + -6.42857143 = 2.045403014 Simplifying x + -6.42857143 = 2.045403014 Reorder the terms: -6.42857143 + x = 2.045403014 Solving -6.42857143 + x = 2.045403014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + x = 2.045403014 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + x = 2.045403014 + 6.42857143 x = 2.045403014 + 6.42857143 Combine like terms: 2.045403014 + 6.42857143 = 8.473974444 x = 8.473974444 Simplifying x = 8.473974444Subproblem 2
x + -6.42857143 = -2.045403014 Simplifying x + -6.42857143 = -2.045403014 Reorder the terms: -6.42857143 + x = -2.045403014 Solving -6.42857143 + x = -2.045403014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + x = -2.045403014 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + x = -2.045403014 + 6.42857143 x = -2.045403014 + 6.42857143 Combine like terms: -2.045403014 + 6.42857143 = 4.383168416 x = 4.383168416 Simplifying x = 4.383168416Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.473974444, 4.383168416}
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