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Simplifying 10x2 + 6x + -2x2 + x + -6 = 0 Reorder the terms: -6 + 6x + x + 10x2 + -2x2 = 0 Combine like terms: 6x + x = 7x -6 + 7x + 10x2 + -2x2 = 0 Combine like terms: 10x2 + -2x2 = 8x2 -6 + 7x + 8x2 = 0 Solving -6 + 7x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + 0.875x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.875x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.875x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.875x + x2 = 0 + 0.75 0.875x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.875x + x2 = 0.75 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = 0.75 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = 0.75 + 0.19140625 Combine like terms: 0.75 + 0.19140625 = 0.94140625 0.19140625 + 0.875x + x2 = 0.94140625 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 0.94140625 Calculate the square root of the right side: 0.970260919 Break this problem into two subproblems by setting (x + 0.4375) equal to 0.970260919 and -0.970260919.Subproblem 1
x + 0.4375 = 0.970260919 Simplifying x + 0.4375 = 0.970260919 Reorder the terms: 0.4375 + x = 0.970260919 Solving 0.4375 + x = 0.970260919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 0.970260919 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 0.970260919 + -0.4375 x = 0.970260919 + -0.4375 Combine like terms: 0.970260919 + -0.4375 = 0.532760919 x = 0.532760919 Simplifying x = 0.532760919Subproblem 2
x + 0.4375 = -0.970260919 Simplifying x + 0.4375 = -0.970260919 Reorder the terms: 0.4375 + x = -0.970260919 Solving 0.4375 + x = -0.970260919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -0.970260919 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -0.970260919 + -0.4375 x = -0.970260919 + -0.4375 Combine like terms: -0.970260919 + -0.4375 = -1.407760919 x = -1.407760919 Simplifying x = -1.407760919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.532760919, -1.407760919}
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