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Simplifying 10x2 + -11x + -80 = 0 Reorder the terms: -80 + -11x + 10x2 = 0 Solving -80 + -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'. -8 + -1.1x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -1.1x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -1.1x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1.1x + x2 = 0 + 8 -1.1x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -1.1x + x2 = 8 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 = 8 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 8 + 0.3025 Combine like terms: 8 + 0.3025 = 8.3025 0.3025 + -1.1x + x2 = 8.3025 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 8.3025 Calculate the square root of the right side: 2.881405907 Break this problem into two subproblems by setting (x + -0.55) equal to 2.881405907 and -2.881405907.Subproblem 1
x + -0.55 = 2.881405907 Simplifying x + -0.55 = 2.881405907 Reorder the terms: -0.55 + x = 2.881405907 Solving -0.55 + x = 2.881405907 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 = 2.881405907 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 2.881405907 + 0.55 x = 2.881405907 + 0.55 Combine like terms: 2.881405907 + 0.55 = 3.431405907 x = 3.431405907 Simplifying x = 3.431405907Subproblem 2
x + -0.55 = -2.881405907 Simplifying x + -0.55 = -2.881405907 Reorder the terms: -0.55 + x = -2.881405907 Solving -0.55 + x = -2.881405907 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 = -2.881405907 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -2.881405907 + 0.55 x = -2.881405907 + 0.55 Combine like terms: -2.881405907 + 0.55 = -2.331405907 x = -2.331405907 Simplifying x = -2.331405907Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.431405907, -2.331405907}
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