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Simplifying 4x2 + 7x + -16 = 0 Reorder the terms: -16 + 7x + 4x2 = 0 Solving -16 + 7x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4 + 1.75x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.75x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.75x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.75x + x2 = 0 + 4 1.75x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.75x + x2 = 4 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 4 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 4 + 0.765625 Combine like terms: 4 + 0.765625 = 4.765625 0.765625 + 1.75x + x2 = 4.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 4.765625 Calculate the square root of the right side: 2.18303115 Break this problem into two subproblems by setting (x + 0.875) equal to 2.18303115 and -2.18303115.Subproblem 1
x + 0.875 = 2.18303115 Simplifying x + 0.875 = 2.18303115 Reorder the terms: 0.875 + x = 2.18303115 Solving 0.875 + x = 2.18303115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 2.18303115 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.18303115 + -0.875 x = 2.18303115 + -0.875 Combine like terms: 2.18303115 + -0.875 = 1.30803115 x = 1.30803115 Simplifying x = 1.30803115Subproblem 2
x + 0.875 = -2.18303115 Simplifying x + 0.875 = -2.18303115 Reorder the terms: 0.875 + x = -2.18303115 Solving 0.875 + x = -2.18303115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -2.18303115 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.18303115 + -0.875 x = -2.18303115 + -0.875 Combine like terms: -2.18303115 + -0.875 = -3.05803115 x = -3.05803115 Simplifying x = -3.05803115Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.30803115, -3.05803115}
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