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Simplifying f(0) = 4x2 + 2x + -4 Reorder the terms for easier multiplication: 0f = 4x2 + 2x + -4 Anything times zero is zero. 0f = 4x2 + 2x + -4 Reorder the terms: 0 = -4 + 2x + 4x2 Solving 0 = -4 + 2x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 4 = 4 4 + -2x + -4x2 = -4 + 2x + 4x2 + 4 + -2x + -4x2 Reorder the terms: 4 + -2x + -4x2 = -4 + 4 + 2x + -2x + 4x2 + -4x2 Combine like terms: -4 + 4 = 0 4 + -2x + -4x2 = 0 + 2x + -2x + 4x2 + -4x2 4 + -2x + -4x2 = 2x + -2x + 4x2 + -4x2 Combine like terms: 2x + -2x = 0 4 + -2x + -4x2 = 0 + 4x2 + -4x2 4 + -2x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 4 + -2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -1x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1x + -2x2)' equal to zero and attempt to solve: Simplifying 2 + -1x + -2x2 = 0 Solving 2 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + 0.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.5x + x2 = 0 + 1 0.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.5x + x2 = 1 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + 0.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 0.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 0.25 = 1.030776406 Simplifying x + 0.25 = 1.030776406 Reorder the terms: 0.25 + x = 1.030776406 Solving 0.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.030776406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.030776406 + -0.25 x = 1.030776406 + -0.25 Combine like terms: 1.030776406 + -0.25 = 0.780776406 x = 0.780776406 Simplifying x = 0.780776406Subproblem 2
x + 0.25 = -1.030776406 Simplifying x + 0.25 = -1.030776406 Reorder the terms: 0.25 + x = -1.030776406 Solving 0.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.030776406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.030776406 + -0.25 x = -1.030776406 + -0.25 Combine like terms: -1.030776406 + -0.25 = -1.280776406 x = -1.280776406 Simplifying x = -1.280776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.780776406, -1.280776406}Solution
x = {0.780776406, -1.280776406}
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