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Simplifying 10x3 + -23x2 + -4x = 0 Reorder the terms: -4x + -23x2 + 10x3 = 0 Solving -4x + -23x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + -23x + 10x2) = 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 '(-4 + -23x + 10x2)' equal to zero and attempt to solve: Simplifying -4 + -23x + 10x2 = 0 Solving -4 + -23x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + -2.3x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -2.3x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -2.3x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -2.3x + x2 = 0 + 0.4 -2.3x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -2.3x + x2 = 0.4 The x term is -2.3x. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3x + 1.3225 + x2 = 0.4 + 1.3225 Reorder the terms: 1.3225 + -2.3x + x2 = 0.4 + 1.3225 Combine like terms: 0.4 + 1.3225 = 1.7225 1.3225 + -2.3x + x2 = 1.7225 Factor a perfect square on the left side: (x + -1.15)(x + -1.15) = 1.7225 Calculate the square root of the right side: 1.312440475 Break this problem into two subproblems by setting (x + -1.15) equal to 1.312440475 and -1.312440475.Subproblem 1
x + -1.15 = 1.312440475 Simplifying x + -1.15 = 1.312440475 Reorder the terms: -1.15 + x = 1.312440475 Solving -1.15 + x = 1.312440475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = 1.312440475 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = 1.312440475 + 1.15 x = 1.312440475 + 1.15 Combine like terms: 1.312440475 + 1.15 = 2.462440475 x = 2.462440475 Simplifying x = 2.462440475Subproblem 2
x + -1.15 = -1.312440475 Simplifying x + -1.15 = -1.312440475 Reorder the terms: -1.15 + x = -1.312440475 Solving -1.15 + x = -1.312440475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = -1.312440475 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = -1.312440475 + 1.15 x = -1.312440475 + 1.15 Combine like terms: -1.312440475 + 1.15 = -0.162440475 x = -0.162440475 Simplifying x = -0.162440475Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.462440475, -0.162440475}Solution
x = {0, 2.462440475, -0.162440475}
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