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Simplifying 4x2 + -15x + -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 = 4.835679821 x = 4.835679821 Simplifying x = 4.835679821Subproblem 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 = -1.085679821 x = -1.085679821 Simplifying x = -1.085679821Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.835679821, -1.085679821}
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