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Simplifying 0 = 4x2 + 10.34x + -4.57 Reorder the terms: 0 = -4.57 + 10.34x + 4x2 Solving 0 = -4.57 + 10.34x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 4.57 = 4.57 4.57 + -10.34x + -4x2 = -4.57 + 10.34x + 4x2 + 4.57 + -10.34x + -4x2 Reorder the terms: 4.57 + -10.34x + -4x2 = -4.57 + 4.57 + 10.34x + -10.34x + 4x2 + -4x2 Combine like terms: -4.57 + 4.57 = 0.00 4.57 + -10.34x + -4x2 = 0.00 + 10.34x + -10.34x + 4x2 + -4x2 4.57 + -10.34x + -4x2 = 10.34x + -10.34x + 4x2 + -4x2 Combine like terms: 10.34x + -10.34x = 0.00 4.57 + -10.34x + -4x2 = 0.00 + 4x2 + -4x2 4.57 + -10.34x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 4.57 + -10.34x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.1425 + 2.585x + x2 = 0 Move the constant term to the right: Add '1.1425' to each side of the equation. -1.1425 + 2.585x + 1.1425 + x2 = 0 + 1.1425 Reorder the terms: -1.1425 + 1.1425 + 2.585x + x2 = 0 + 1.1425 Combine like terms: -1.1425 + 1.1425 = 0.0000 0.0000 + 2.585x + x2 = 0 + 1.1425 2.585x + x2 = 0 + 1.1425 Combine like terms: 0 + 1.1425 = 1.1425 2.585x + x2 = 1.1425 The x term is 2.585x. Take half its coefficient (1.2925). Square it (1.67055625) and add it to both sides. Add '1.67055625' to each side of the equation. 2.585x + 1.67055625 + x2 = 1.1425 + 1.67055625 Reorder the terms: 1.67055625 + 2.585x + x2 = 1.1425 + 1.67055625 Combine like terms: 1.1425 + 1.67055625 = 2.81305625 1.67055625 + 2.585x + x2 = 2.81305625 Factor a perfect square on the left side: (x + 1.2925)(x + 1.2925) = 2.81305625 Calculate the square root of the right side: 1.677216817 Break this problem into two subproblems by setting (x + 1.2925) equal to 1.677216817 and -1.677216817.Subproblem 1
x + 1.2925 = 1.677216817 Simplifying x + 1.2925 = 1.677216817 Reorder the terms: 1.2925 + x = 1.677216817 Solving 1.2925 + x = 1.677216817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2925' to each side of the equation. 1.2925 + -1.2925 + x = 1.677216817 + -1.2925 Combine like terms: 1.2925 + -1.2925 = 0.0000 0.0000 + x = 1.677216817 + -1.2925 x = 1.677216817 + -1.2925 Combine like terms: 1.677216817 + -1.2925 = 0.384716817 x = 0.384716817 Simplifying x = 0.384716817Subproblem 2
x + 1.2925 = -1.677216817 Simplifying x + 1.2925 = -1.677216817 Reorder the terms: 1.2925 + x = -1.677216817 Solving 1.2925 + x = -1.677216817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2925' to each side of the equation. 1.2925 + -1.2925 + x = -1.677216817 + -1.2925 Combine like terms: 1.2925 + -1.2925 = 0.0000 0.0000 + x = -1.677216817 + -1.2925 x = -1.677216817 + -1.2925 Combine like terms: -1.677216817 + -1.2925 = -2.969716817 x = -2.969716817 Simplifying x = -2.969716817Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.384716817, -2.969716817}
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