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Simplifying f(0) = 4x2 + 3x + -4 Reorder the terms for easier multiplication: 0f = 4x2 + 3x + -4 Anything times zero is zero. 0f = 4x2 + 3x + -4 Reorder the terms: 0 = -4 + 3x + 4x2 Solving 0 = -4 + 3x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 4 = 4 4 + -3x + -4x2 = -4 + 3x + 4x2 + 4 + -3x + -4x2 Reorder the terms: 4 + -3x + -4x2 = -4 + 4 + 3x + -3x + 4x2 + -4x2 Combine like terms: -4 + 4 = 0 4 + -3x + -4x2 = 0 + 3x + -3x + 4x2 + -4x2 4 + -3x + -4x2 = 3x + -3x + 4x2 + -4x2 Combine like terms: 3x + -3x = 0 4 + -3x + -4x2 = 0 + 4x2 + -4x2 4 + -3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 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 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 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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