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Simplifying 3x(4x + -3) = 10x + -1 Reorder the terms: 3x(-3 + 4x) = 10x + -1 (-3 * 3x + 4x * 3x) = 10x + -1 (-9x + 12x2) = 10x + -1 Reorder the terms: -9x + 12x2 = -1 + 10x Solving -9x + 12x2 = -1 + 10x Solving for variable 'x'. Reorder the terms: 1 + -9x + -10x + 12x2 = -1 + 10x + 1 + -10x Combine like terms: -9x + -10x = -19x 1 + -19x + 12x2 = -1 + 10x + 1 + -10x Reorder the terms: 1 + -19x + 12x2 = -1 + 1 + 10x + -10x Combine like terms: -1 + 1 = 0 1 + -19x + 12x2 = 0 + 10x + -10x 1 + -19x + 12x2 = 10x + -10x Combine like terms: 10x + -10x = 0 1 + -19x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.08333333333 + -1.583333333x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + -1.583333333x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + -1.583333333x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + -1.583333333x + x2 = 0 + -0.08333333333 -1.583333333x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 -1.583333333x + x2 = -0.08333333333 The x term is -1.583333333x. Take half its coefficient (-0.7916666665). Square it (0.6267361108) and add it to both sides. Add '0.6267361108' to each side of the equation. -1.583333333x + 0.6267361108 + x2 = -0.08333333333 + 0.6267361108 Reorder the terms: 0.6267361108 + -1.583333333x + x2 = -0.08333333333 + 0.6267361108 Combine like terms: -0.08333333333 + 0.6267361108 = 0.54340277747 0.6267361108 + -1.583333333x + x2 = 0.54340277747 Factor a perfect square on the left side: (x + -0.7916666665)(x + -0.7916666665) = 0.54340277747 Calculate the square root of the right side: 0.737158584 Break this problem into two subproblems by setting (x + -0.7916666665) equal to 0.737158584 and -0.737158584.Subproblem 1
x + -0.7916666665 = 0.737158584 Simplifying x + -0.7916666665 = 0.737158584 Reorder the terms: -0.7916666665 + x = 0.737158584 Solving -0.7916666665 + x = 0.737158584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + x = 0.737158584 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + x = 0.737158584 + 0.7916666665 x = 0.737158584 + 0.7916666665 Combine like terms: 0.737158584 + 0.7916666665 = 1.5288252505 x = 1.5288252505 Simplifying x = 1.5288252505Subproblem 2
x + -0.7916666665 = -0.737158584 Simplifying x + -0.7916666665 = -0.737158584 Reorder the terms: -0.7916666665 + x = -0.737158584 Solving -0.7916666665 + x = -0.737158584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + x = -0.737158584 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + x = -0.737158584 + 0.7916666665 x = -0.737158584 + 0.7916666665 Combine like terms: -0.737158584 + 0.7916666665 = 0.0545080825 x = 0.0545080825 Simplifying x = 0.0545080825Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5288252505, 0.0545080825}
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