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Simplifying x(4x + 15) + -21 = 0 Reorder the terms: x(15 + 4x) + -21 = 0 (15 * x + 4x * x) + -21 = 0 (15x + 4x2) + -21 = 0 Reorder the terms: -21 + 15x + 4x2 = 0 Solving -21 + 15x + 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'. -5.25 + 3.75x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 3.75x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 3.75x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 3.75x + x2 = 0 + 5.25 3.75x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 3.75x + x2 = 5.25 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 5.25 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 5.25 + 3.515625 Combine like terms: 5.25 + 3.515625 = 8.765625 3.515625 + 3.75x + x2 = 8.765625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 8.765625 Calculate the square root of the right side: 2.960679821 Break this problem into two subproblems by setting (x + 1.875) equal to 2.960679821 and -2.960679821.Subproblem 1
x + 1.875 = 2.960679821 Simplifying x + 1.875 = 2.960679821 Reorder the terms: 1.875 + x = 2.960679821 Solving 1.875 + x = 2.960679821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 2.960679821 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 2.960679821 + -1.875 x = 2.960679821 + -1.875 Combine like terms: 2.960679821 + -1.875 = 1.085679821 x = 1.085679821 Simplifying x = 1.085679821Subproblem 2
x + 1.875 = -2.960679821 Simplifying x + 1.875 = -2.960679821 Reorder the terms: 1.875 + x = -2.960679821 Solving 1.875 + x = -2.960679821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -2.960679821 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -2.960679821 + -1.875 x = -2.960679821 + -1.875 Combine like terms: -2.960679821 + -1.875 = -4.835679821 x = -4.835679821 Simplifying x = -4.835679821Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.085679821, -4.835679821}
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