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Simplifying 10x2 + -27x + 10 = 0 Reorder the terms: 10 + -27x + 10x2 = 0 Solving 10 + -27x + 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'. 1 + -2.7x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.7x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.7x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.7x + x2 = 0 + -1 -2.7x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.7x + x2 = -1 The x term is -2.7x. Take half its coefficient (-1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. -2.7x + 1.8225 + x2 = -1 + 1.8225 Reorder the terms: 1.8225 + -2.7x + x2 = -1 + 1.8225 Combine like terms: -1 + 1.8225 = 0.8225 1.8225 + -2.7x + x2 = 0.8225 Factor a perfect square on the left side: (x + -1.35)(x + -1.35) = 0.8225 Calculate the square root of the right side: 0.906917857 Break this problem into two subproblems by setting (x + -1.35) equal to 0.906917857 and -0.906917857.Subproblem 1
x + -1.35 = 0.906917857 Simplifying x + -1.35 = 0.906917857 Reorder the terms: -1.35 + x = 0.906917857 Solving -1.35 + x = 0.906917857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = 0.906917857 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = 0.906917857 + 1.35 x = 0.906917857 + 1.35 Combine like terms: 0.906917857 + 1.35 = 2.256917857 x = 2.256917857 Simplifying x = 2.256917857Subproblem 2
x + -1.35 = -0.906917857 Simplifying x + -1.35 = -0.906917857 Reorder the terms: -1.35 + x = -0.906917857 Solving -1.35 + x = -0.906917857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = -0.906917857 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = -0.906917857 + 1.35 x = -0.906917857 + 1.35 Combine like terms: -0.906917857 + 1.35 = 0.443082143 x = 0.443082143 Simplifying x = 0.443082143Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.256917857, 0.443082143}
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