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Simplifying 10x2 + -11x + -26 = 0 Reorder the terms: -26 + -11x + 10x2 = 0 Solving -26 + -11x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.6 + -1.1x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -1.1x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -1.1x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -1.1x + x2 = 0 + 2.6 -1.1x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -1.1x + x2 = 2.6 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = 2.6 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 2.6 + 0.3025 Combine like terms: 2.6 + 0.3025 = 2.9025 0.3025 + -1.1x + x2 = 2.9025 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 2.9025 Calculate the square root of the right side: 1.703672504 Break this problem into two subproblems by setting (x + -0.55) equal to 1.703672504 and -1.703672504.Subproblem 1
x + -0.55 = 1.703672504 Simplifying x + -0.55 = 1.703672504 Reorder the terms: -0.55 + x = 1.703672504 Solving -0.55 + x = 1.703672504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 1.703672504 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 1.703672504 + 0.55 x = 1.703672504 + 0.55 Combine like terms: 1.703672504 + 0.55 = 2.253672504 x = 2.253672504 Simplifying x = 2.253672504Subproblem 2
x + -0.55 = -1.703672504 Simplifying x + -0.55 = -1.703672504 Reorder the terms: -0.55 + x = -1.703672504 Solving -0.55 + x = -1.703672504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -1.703672504 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -1.703672504 + 0.55 x = -1.703672504 + 0.55 Combine like terms: -1.703672504 + 0.55 = -1.153672504 x = -1.153672504 Simplifying x = -1.153672504Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.253672504, -1.153672504}
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