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Simplifying -19x3 + -13x2 + 16x = 0 Reorder the terms: 16x + -13x2 + -19x3 = 0 Solving 16x + -13x2 + -19x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(16 + -13x + -19x2) = 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 '(16 + -13x + -19x2)' equal to zero and attempt to solve: Simplifying 16 + -13x + -19x2 = 0 Solving 16 + -13x + -19x2 = 0 Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. -0.8421052632 + 0.6842105263x + x2 = 0 Move the constant term to the right: Add '0.8421052632' to each side of the equation. -0.8421052632 + 0.6842105263x + 0.8421052632 + x2 = 0 + 0.8421052632 Reorder the terms: -0.8421052632 + 0.8421052632 + 0.6842105263x + x2 = 0 + 0.8421052632 Combine like terms: -0.8421052632 + 0.8421052632 = 0.0000000000 0.0000000000 + 0.6842105263x + x2 = 0 + 0.8421052632 0.6842105263x + x2 = 0 + 0.8421052632 Combine like terms: 0 + 0.8421052632 = 0.8421052632 0.6842105263x + x2 = 0.8421052632 The x term is 0.6842105263x. Take half its coefficient (0.3421052632). Square it (0.1170360111) and add it to both sides. Add '0.1170360111' to each side of the equation. 0.6842105263x + 0.1170360111 + x2 = 0.8421052632 + 0.1170360111 Reorder the terms: 0.1170360111 + 0.6842105263x + x2 = 0.8421052632 + 0.1170360111 Combine like terms: 0.8421052632 + 0.1170360111 = 0.9591412743 0.1170360111 + 0.6842105263x + x2 = 0.9591412743 Factor a perfect square on the left side: (x + 0.3421052632)(x + 0.3421052632) = 0.9591412743 Calculate the square root of the right side: 0.979357582 Break this problem into two subproblems by setting (x + 0.3421052632) equal to 0.979357582 and -0.979357582.Subproblem 1
x + 0.3421052632 = 0.979357582 Simplifying x + 0.3421052632 = 0.979357582 Reorder the terms: 0.3421052632 + x = 0.979357582 Solving 0.3421052632 + x = 0.979357582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3421052632' to each side of the equation. 0.3421052632 + -0.3421052632 + x = 0.979357582 + -0.3421052632 Combine like terms: 0.3421052632 + -0.3421052632 = 0.0000000000 0.0000000000 + x = 0.979357582 + -0.3421052632 x = 0.979357582 + -0.3421052632 Combine like terms: 0.979357582 + -0.3421052632 = 0.6372523188 x = 0.6372523188 Simplifying x = 0.6372523188Subproblem 2
x + 0.3421052632 = -0.979357582 Simplifying x + 0.3421052632 = -0.979357582 Reorder the terms: 0.3421052632 + x = -0.979357582 Solving 0.3421052632 + x = -0.979357582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3421052632' to each side of the equation. 0.3421052632 + -0.3421052632 + x = -0.979357582 + -0.3421052632 Combine like terms: 0.3421052632 + -0.3421052632 = 0.0000000000 0.0000000000 + x = -0.979357582 + -0.3421052632 x = -0.979357582 + -0.3421052632 Combine like terms: -0.979357582 + -0.3421052632 = -1.3214628452 x = -1.3214628452 Simplifying x = -1.3214628452Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6372523188, -1.3214628452}Solution
x = {0, 0.6372523188, -1.3214628452}
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