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Simplifying 4x3 + -13x2 = 3x Reorder the terms: -13x2 + 4x3 = 3x Solving -13x2 + 4x3 = 3x Solving for variable 'x'. Reorder the terms: -3x + -13x2 + 4x3 = 3x + -3x Combine like terms: 3x + -3x = 0 -3x + -13x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + -13x + 4x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-3 + -13x + 4x2)' equal to zero and attempt to solve: Simplifying -3 + -13x + 4x2 = 0 Solving -3 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -3.25x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -3.25x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -3.25x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -3.25x + x2 = 0 + 0.75 -3.25x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -3.25x + x2 = 0.75 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 0.75 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 0.75 + 2.640625 Combine like terms: 0.75 + 2.640625 = 3.390625 2.640625 + -3.25x + x2 = 3.390625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (x + -1.625) equal to 1.841364983 and -1.841364983.Subproblem 1
x + -1.625 = 1.841364983 Simplifying x + -1.625 = 1.841364983 Reorder the terms: -1.625 + x = 1.841364983 Solving -1.625 + x = 1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 1.841364983 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.841364983 + 1.625 x = 1.841364983 + 1.625 Combine like terms: 1.841364983 + 1.625 = 3.466364983 x = 3.466364983 Simplifying x = 3.466364983Subproblem 2
x + -1.625 = -1.841364983 Simplifying x + -1.625 = -1.841364983 Reorder the terms: -1.625 + x = -1.841364983 Solving -1.625 + x = -1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -1.841364983 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.841364983 + 1.625 x = -1.841364983 + 1.625 Combine like terms: -1.841364983 + 1.625 = -0.216364983 x = -0.216364983 Simplifying x = -0.216364983Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.466364983, -0.216364983}Solution
x = {0, 3.466364983, -0.216364983}
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