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Simplifying 10x3 + 12x2 + -14x = 0 Reorder the terms: -14x + 12x2 + 10x3 = 0 Solving -14x + 12x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-7 + 6x + 5x2) = 0 Ignore the factor 2.Subproblem 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 '(-7 + 6x + 5x2)' equal to zero and attempt to solve: Simplifying -7 + 6x + 5x2 = 0 Solving -7 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 1.2x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 1.2x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 1.2x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 1.2x + x2 = 0 + 1.4 1.2x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 1.2x + x2 = 1.4 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 1.4 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 1.4 + 0.36 Combine like terms: 1.4 + 0.36 = 1.76 0.36 + 1.2x + x2 = 1.76 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (x + 0.6) equal to 1.326649916 and -1.326649916.Subproblem 1
x + 0.6 = 1.326649916 Simplifying x + 0.6 = 1.326649916 Reorder the terms: 0.6 + x = 1.326649916 Solving 0.6 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 1.326649916 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.326649916 + -0.6 x = 1.326649916 + -0.6 Combine like terms: 1.326649916 + -0.6 = 0.726649916 x = 0.726649916 Simplifying x = 0.726649916Subproblem 2
x + 0.6 = -1.326649916 Simplifying x + 0.6 = -1.326649916 Reorder the terms: 0.6 + x = -1.326649916 Solving 0.6 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -1.326649916 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.326649916 + -0.6 x = -1.326649916 + -0.6 Combine like terms: -1.326649916 + -0.6 = -1.926649916 x = -1.926649916 Simplifying x = -1.926649916Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.726649916, -1.926649916}Solution
x = {0, 0.726649916, -1.926649916}
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