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Simplifying 0 = (5x2 + -4x + -16) Reorder the terms: 0 = (-16 + -4x + 5x2) Remove parenthesis around (-16 + -4x + 5x2) 0 = -16 + -4x + 5x2 Solving 0 = -16 + -4x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 16 = 16 16 + 4x + -5x2 = -16 + -4x + 5x2 + 16 + 4x + -5x2 Reorder the terms: 16 + 4x + -5x2 = -16 + 16 + -4x + 4x + 5x2 + -5x2 Combine like terms: -16 + 16 = 0 16 + 4x + -5x2 = 0 + -4x + 4x + 5x2 + -5x2 16 + 4x + -5x2 = -4x + 4x + 5x2 + -5x2 Combine like terms: -4x + 4x = 0 16 + 4x + -5x2 = 0 + 5x2 + -5x2 16 + 4x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 16 + 4x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.2 + -0.8x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -0.8x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -0.8x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -0.8x + x2 = 0 + 3.2 -0.8x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -0.8x + x2 = 3.2 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 3.2 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 3.2 + 0.16 Combine like terms: 3.2 + 0.16 = 3.36 0.16 + -0.8x + x2 = 3.36 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 3.36 Calculate the square root of the right side: 1.833030278 Break this problem into two subproblems by setting (x + -0.4) equal to 1.833030278 and -1.833030278.Subproblem 1
x + -0.4 = 1.833030278 Simplifying x + -0.4 = 1.833030278 Reorder the terms: -0.4 + x = 1.833030278 Solving -0.4 + x = 1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.833030278 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.833030278 + 0.4 x = 1.833030278 + 0.4 Combine like terms: 1.833030278 + 0.4 = 2.233030278 x = 2.233030278 Simplifying x = 2.233030278Subproblem 2
x + -0.4 = -1.833030278 Simplifying x + -0.4 = -1.833030278 Reorder the terms: -0.4 + x = -1.833030278 Solving -0.4 + x = -1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.833030278 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.833030278 + 0.4 x = -1.833030278 + 0.4 Combine like terms: -1.833030278 + 0.4 = -1.433030278 x = -1.433030278 Simplifying x = -1.433030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.233030278, -1.433030278}
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