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Simplifying 14x3 + -8x2 + -18x = 0 Reorder the terms: -18x + -8x2 + 14x3 = 0 Solving -18x + -8x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-9 + -4x + 7x2) = 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 '(-9 + -4x + 7x2)' equal to zero and attempt to solve: Simplifying -9 + -4x + 7x2 = 0 Solving -9 + -4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -0.5714285714x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -0.5714285714x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -0.5714285714x + x2 = 0 + 1.285714286 -0.5714285714x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -0.5714285714x + x2 = 1.285714286 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 1.285714286 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 1.285714286 + 0.08163265305 Combine like terms: 1.285714286 + 0.08163265305 = 1.36734693905 0.08163265305 + -0.5714285714x + x2 = 1.36734693905 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 1.36734693905 Calculate the square root of the right side: 1.16933611 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 1.16933611 and -1.16933611.Subproblem 1
x + -0.2857142857 = 1.16933611 Simplifying x + -0.2857142857 = 1.16933611 Reorder the terms: -0.2857142857 + x = 1.16933611 Solving -0.2857142857 + x = 1.16933611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 1.16933611 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 1.16933611 + 0.2857142857 x = 1.16933611 + 0.2857142857 Combine like terms: 1.16933611 + 0.2857142857 = 1.4550503957 x = 1.4550503957 Simplifying x = 1.4550503957Subproblem 2
x + -0.2857142857 = -1.16933611 Simplifying x + -0.2857142857 = -1.16933611 Reorder the terms: -0.2857142857 + x = -1.16933611 Solving -0.2857142857 + x = -1.16933611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -1.16933611 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -1.16933611 + 0.2857142857 x = -1.16933611 + 0.2857142857 Combine like terms: -1.16933611 + 0.2857142857 = -0.8836218243 x = -0.8836218243 Simplifying x = -0.8836218243Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4550503957, -0.8836218243}Solution
x = {0, 1.4550503957, -0.8836218243}
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