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Simplifying x2 + 0.8x + -4.16 = 0 Reorder the terms: -4.16 + 0.8x + x2 = 0 Solving -4.16 + 0.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4.16' to each side of the equation. -4.16 + 0.8x + 4.16 + x2 = 0 + 4.16 Reorder the terms: -4.16 + 4.16 + 0.8x + x2 = 0 + 4.16 Combine like terms: -4.16 + 4.16 = 0.00 0.00 + 0.8x + x2 = 0 + 4.16 0.8x + x2 = 0 + 4.16 Combine like terms: 0 + 4.16 = 4.16 0.8x + x2 = 4.16 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 4.16 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 4.16 + 0.16 Combine like terms: 4.16 + 0.16 = 4.32 0.16 + 0.8x + x2 = 4.32 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 4.32 Calculate the square root of the right side: 2.078460969 Break this problem into two subproblems by setting (x + 0.4) equal to 2.078460969 and -2.078460969.Subproblem 1
x + 0.4 = 2.078460969 Simplifying x + 0.4 = 2.078460969 Reorder the terms: 0.4 + x = 2.078460969 Solving 0.4 + x = 2.078460969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.078460969 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.078460969 + -0.4 x = 2.078460969 + -0.4 Combine like terms: 2.078460969 + -0.4 = 1.678460969 x = 1.678460969 Simplifying x = 1.678460969Subproblem 2
x + 0.4 = -2.078460969 Simplifying x + 0.4 = -2.078460969 Reorder the terms: 0.4 + x = -2.078460969 Solving 0.4 + x = -2.078460969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.078460969 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.078460969 + -0.4 x = -2.078460969 + -0.4 Combine like terms: -2.078460969 + -0.4 = -2.478460969 x = -2.478460969 Simplifying x = -2.478460969Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.678460969, -2.478460969}
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