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Simplifying (4x2) + (3x) + (1) = 5 (4x2) + (3x) + 1 = 5 Reorder the terms: 1 + (3x) + (4x2) = 5 Solving 1 + (3x) + (4x2) = 5 Solving for variable 'x'. Reorder the terms: 1 + -5 + (3x) + (4x2) = 5 + -5 Combine like terms: 1 + -5 = -4 -4 + (3x) + (4x2) = 5 + -5 Combine like terms: 5 + -5 = 0 -4 + (3x) + (4x2) = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + (0.75x) + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + (0.75x) + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + (0.75x) + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + (0.75x) + x2 = 0 + 1 (0.75x) + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 (0.75x) + x2 = 1 The x term is (0.75x). Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. (0.75x) + 0.140625 + x2 = 1 + 0.140625 Reorder the terms: 0.140625 + (0.75x) + x2 = 1 + 0.140625 Combine like terms: 1 + 0.140625 = 1.140625 0.140625 + (0.75x) + x2 = 1.140625 Factor a perfect square on the left side: ((x) + 0.375)((x) + 0.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting ((x) + 0.375) equal to 1.068000468 and -1.068000468.Subproblem 1
(x) + 0.375 = 1.068000468 Simplifying (x) + 0.375 = 1.068000468 x + 0.375 = 1.068000468 Reorder the terms: 0.375 + x = 1.068000468 Solving 0.375 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.068000468 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.068000468 + -0.375 x = 1.068000468 + -0.375 Combine like terms: 1.068000468 + -0.375 = 0.693000468 x = 0.693000468 Simplifying x = 0.693000468Subproblem 2
(x) + 0.375 = -1.068000468 Simplifying (x) + 0.375 = -1.068000468 x + 0.375 = -1.068000468 Reorder the terms: 0.375 + x = -1.068000468 Solving 0.375 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.068000468 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.068000468 + -0.375 x = -1.068000468 + -0.375 Combine like terms: -1.068000468 + -0.375 = -1.443000468 x = -1.443000468 Simplifying x = -1.443000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.693000468, -1.443000468}
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