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Simplifying 14x4 + 21x3 + -49x2 = 0 Reorder the terms: -49x2 + 21x3 + 14x4 = 0 Solving -49x2 + 21x3 + 14x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7x2'. 7x2(-7 + 3x + 2x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-7 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -7 + 3x + 2x2 = 0 Solving -7 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 1.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 1.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 1.5x + x2 = 0 + 3.5 1.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 1.5x + x2 = 3.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 3.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 3.5 + 0.5625 Combine like terms: 3.5 + 0.5625 = 4.0625 0.5625 + 1.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + 0.75) equal to 2.015564437 and -2.015564437.Subproblem 1
x + 0.75 = 2.015564437 Simplifying x + 0.75 = 2.015564437 Reorder the terms: 0.75 + x = 2.015564437 Solving 0.75 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.015564437 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.015564437 + -0.75 x = 2.015564437 + -0.75 Combine like terms: 2.015564437 + -0.75 = 1.265564437 x = 1.265564437 Simplifying x = 1.265564437Subproblem 2
x + 0.75 = -2.015564437 Simplifying x + 0.75 = -2.015564437 Reorder the terms: 0.75 + x = -2.015564437 Solving 0.75 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.015564437 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.015564437 + -0.75 x = -2.015564437 + -0.75 Combine like terms: -2.015564437 + -0.75 = -2.765564437 x = -2.765564437 Simplifying x = -2.765564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.265564437, -2.765564437}Solution
x = {0, 1.265564437, -2.765564437}
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