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Simplifying 10x3 + -18x2 + -14x = 0 Reorder the terms: -14x + -18x2 + 10x3 = 0 Solving -14x + -18x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-7 + -9x + 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 + -9x + 5x2)' equal to zero and attempt to solve: Simplifying -7 + -9x + 5x2 = 0 Solving -7 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -1.8x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -1.8x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -1.8x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -1.8x + x2 = 0 + 1.4 -1.8x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -1.8x + x2 = 1.4 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 1.4 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 1.4 + 0.81 Combine like terms: 1.4 + 0.81 = 2.21 0.81 + -1.8x + x2 = 2.21 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 2.21 Calculate the square root of the right side: 1.486606875 Break this problem into two subproblems by setting (x + -0.9) equal to 1.486606875 and -1.486606875.Subproblem 1
x + -0.9 = 1.486606875 Simplifying x + -0.9 = 1.486606875 Reorder the terms: -0.9 + x = 1.486606875 Solving -0.9 + x = 1.486606875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 1.486606875 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 1.486606875 + 0.9 x = 1.486606875 + 0.9 Combine like terms: 1.486606875 + 0.9 = 2.386606875 x = 2.386606875 Simplifying x = 2.386606875Subproblem 2
x + -0.9 = -1.486606875 Simplifying x + -0.9 = -1.486606875 Reorder the terms: -0.9 + x = -1.486606875 Solving -0.9 + x = -1.486606875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -1.486606875 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -1.486606875 + 0.9 x = -1.486606875 + 0.9 Combine like terms: -1.486606875 + 0.9 = -0.586606875 x = -0.586606875 Simplifying x = -0.586606875Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.386606875, -0.586606875}Solution
x = {0, 2.386606875, -0.586606875}
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