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Simplifying 0.72x2 + -0.18x + -6.3 = 0 Reorder the terms: -6.3 + -0.18x + 0.72x2 = 0 Solving -6.3 + -0.18x + 0.72x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.72 the coefficient of the squared term: Divide each side by '0.72'. -8.75 + -0.25x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -0.25x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -0.25x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -0.25x + x2 = 0 + 8.75 -0.25x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -0.25x + x2 = 8.75 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 8.75 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 8.75 + 0.015625 Combine like terms: 8.75 + 0.015625 = 8.765625 0.015625 + -0.25x + x2 = 8.765625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 8.765625 Calculate the square root of the right side: 2.960679821 Break this problem into two subproblems by setting (x + -0.125) equal to 2.960679821 and -2.960679821.Subproblem 1
x + -0.125 = 2.960679821 Simplifying x + -0.125 = 2.960679821 Reorder the terms: -0.125 + x = 2.960679821 Solving -0.125 + x = 2.960679821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 2.960679821 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 2.960679821 + 0.125 x = 2.960679821 + 0.125 Combine like terms: 2.960679821 + 0.125 = 3.085679821 x = 3.085679821 Simplifying x = 3.085679821Subproblem 2
x + -0.125 = -2.960679821 Simplifying x + -0.125 = -2.960679821 Reorder the terms: -0.125 + x = -2.960679821 Solving -0.125 + x = -2.960679821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -2.960679821 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -2.960679821 + 0.125 x = -2.960679821 + 0.125 Combine like terms: -2.960679821 + 0.125 = -2.835679821 x = -2.835679821 Simplifying x = -2.835679821Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.085679821, -2.835679821}
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