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Simplifying -9x2 + 26x + -10 = 0 Reorder the terms: -10 + 26x + -9x2 = 0 Solving -10 + 26x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 1.111111111 + -2.888888889x + x2 = 0 Move the constant term to the right: Add '-1.111111111' to each side of the equation. 1.111111111 + -2.888888889x + -1.111111111 + x2 = 0 + -1.111111111 Reorder the terms: 1.111111111 + -1.111111111 + -2.888888889x + x2 = 0 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + -2.888888889x + x2 = 0 + -1.111111111 -2.888888889x + x2 = 0 + -1.111111111 Combine like terms: 0 + -1.111111111 = -1.111111111 -2.888888889x + x2 = -1.111111111 The x term is -2.888888889x. Take half its coefficient (-1.444444445). Square it (2.086419755) and add it to both sides. Add '2.086419755' to each side of the equation. -2.888888889x + 2.086419755 + x2 = -1.111111111 + 2.086419755 Reorder the terms: 2.086419755 + -2.888888889x + x2 = -1.111111111 + 2.086419755 Combine like terms: -1.111111111 + 2.086419755 = 0.975308644 2.086419755 + -2.888888889x + x2 = 0.975308644 Factor a perfect square on the left side: (x + -1.444444445)(x + -1.444444445) = 0.975308644 Calculate the square root of the right side: 0.987577159 Break this problem into two subproblems by setting (x + -1.444444445) equal to 0.987577159 and -0.987577159.Subproblem 1
x + -1.444444445 = 0.987577159 Simplifying x + -1.444444445 = 0.987577159 Reorder the terms: -1.444444445 + x = 0.987577159 Solving -1.444444445 + x = 0.987577159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + x = 0.987577159 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = 0.987577159 + 1.444444445 x = 0.987577159 + 1.444444445 Combine like terms: 0.987577159 + 1.444444445 = 2.432021604 x = 2.432021604 Simplifying x = 2.432021604Subproblem 2
x + -1.444444445 = -0.987577159 Simplifying x + -1.444444445 = -0.987577159 Reorder the terms: -1.444444445 + x = -0.987577159 Solving -1.444444445 + x = -0.987577159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + x = -0.987577159 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = -0.987577159 + 1.444444445 x = -0.987577159 + 1.444444445 Combine like terms: -0.987577159 + 1.444444445 = 0.456867286 x = 0.456867286 Simplifying x = 0.456867286Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.432021604, 0.456867286}
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