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Simplifying 5x2 + 12x + -40 = f(0) Reorder the terms: -40 + 12x + 5x2 = f(0) Reorder the terms for easier multiplication: -40 + 12x + 5x2 = 0f Anything times zero is zero. -40 + 12x + 5x2 = 0f Solving -40 + 12x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8 + 2.4x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 2.4x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 2.4x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2.4x + x2 = 0 + 8 2.4x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 2.4x + x2 = 8 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 8 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 8 + 1.44 Combine like terms: 8 + 1.44 = 9.44 1.44 + 2.4x + x2 = 9.44 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 9.44 Calculate the square root of the right side: 3.072458299 Break this problem into two subproblems by setting (x + 1.2) equal to 3.072458299 and -3.072458299.Subproblem 1
x + 1.2 = 3.072458299 Simplifying x + 1.2 = 3.072458299 Reorder the terms: 1.2 + x = 3.072458299 Solving 1.2 + x = 3.072458299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 3.072458299 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 3.072458299 + -1.2 x = 3.072458299 + -1.2 Combine like terms: 3.072458299 + -1.2 = 1.872458299 x = 1.872458299 Simplifying x = 1.872458299Subproblem 2
x + 1.2 = -3.072458299 Simplifying x + 1.2 = -3.072458299 Reorder the terms: 1.2 + x = -3.072458299 Solving 1.2 + x = -3.072458299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -3.072458299 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -3.072458299 + -1.2 x = -3.072458299 + -1.2 Combine like terms: -3.072458299 + -1.2 = -4.272458299 x = -4.272458299 Simplifying x = -4.272458299Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.872458299, -4.272458299}
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