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Simplifying (3x + -0.5) * x = 56.5 Reorder the terms: (-0.5 + 3x) * x = 56.5 Reorder the terms for easier multiplication: x(-0.5 + 3x) = 56.5 (-0.5 * x + 3x * x) = 56.5 (-0.5x + 3x2) = 56.5 Solving -0.5x + 3x2 = 56.5 Solving for variable 'x'. Reorder the terms: -56.5 + -0.5x + 3x2 = 56.5 + -56.5 Combine like terms: 56.5 + -56.5 = 0.0 -56.5 + -0.5x + 3x2 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -18.83333333 + -0.1666666667x + x2 = 0.0 Move the constant term to the right: Add '18.83333333' to each side of the equation. -18.83333333 + -0.1666666667x + 18.83333333 + x2 = 0.0 + 18.83333333 Reorder the terms: -18.83333333 + 18.83333333 + -0.1666666667x + x2 = 0.0 + 18.83333333 Combine like terms: -18.83333333 + 18.83333333 = 0.00000000 0.00000000 + -0.1666666667x + x2 = 0.0 + 18.83333333 -0.1666666667x + x2 = 0.0 + 18.83333333 Combine like terms: 0.0 + 18.83333333 = 18.83333333 -0.1666666667x + x2 = 18.83333333 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 18.83333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 18.83333333 + 0.006944444447 Combine like terms: 18.83333333 + 0.006944444447 = 18.840277774447 0.006944444447 + -0.1666666667x + x2 = 18.840277774447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 18.840277774447 Calculate the square root of the right side: 4.340538881 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 4.340538881 and -4.340538881.Subproblem 1
x + -0.08333333335 = 4.340538881 Simplifying x + -0.08333333335 = 4.340538881 Reorder the terms: -0.08333333335 + x = 4.340538881 Solving -0.08333333335 + x = 4.340538881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 4.340538881 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 4.340538881 + 0.08333333335 x = 4.340538881 + 0.08333333335 Combine like terms: 4.340538881 + 0.08333333335 = 4.42387221435 x = 4.42387221435 Simplifying x = 4.42387221435Subproblem 2
x + -0.08333333335 = -4.340538881 Simplifying x + -0.08333333335 = -4.340538881 Reorder the terms: -0.08333333335 + x = -4.340538881 Solving -0.08333333335 + x = -4.340538881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -4.340538881 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -4.340538881 + 0.08333333335 x = -4.340538881 + 0.08333333335 Combine like terms: -4.340538881 + 0.08333333335 = -4.25720554765 x = -4.25720554765 Simplifying x = -4.25720554765Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.42387221435, -4.25720554765}
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