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Simplifying 0 = 10x3 + 66x2 + 14x Reorder the terms: 0 = 14x + 66x2 + 10x3 Solving 0 = 14x + 66x2 + 10x3 Solving for variable 'x'. Remove the zero: -14x + -66x2 + -10x3 = 14x + 66x2 + 10x3 + -14x + -66x2 + -10x3 Reorder the terms: -14x + -66x2 + -10x3 = 14x + -14x + 66x2 + -66x2 + 10x3 + -10x3 Combine like terms: 14x + -14x = 0 -14x + -66x2 + -10x3 = 0 + 66x2 + -66x2 + 10x3 + -10x3 -14x + -66x2 + -10x3 = 66x2 + -66x2 + 10x3 + -10x3 Combine like terms: 66x2 + -66x2 = 0 -14x + -66x2 + -10x3 = 0 + 10x3 + -10x3 -14x + -66x2 + -10x3 = 10x3 + -10x3 Combine like terms: 10x3 + -10x3 = 0 -14x + -66x2 + -10x3 = 0 Factor out the Greatest Common Factor (GCF), '-2x'. -2x(7 + 33x + 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 + 33x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + 33x + 5x2 = 0 Solving 7 + 33x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 6.6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 6.6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 6.6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 6.6x + x2 = 0 + -1.4 6.6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 6.6x + x2 = -1.4 The x term is 6.6x. Take half its coefficient (3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. 6.6x + 10.89 + x2 = -1.4 + 10.89 Reorder the terms: 10.89 + 6.6x + x2 = -1.4 + 10.89 Combine like terms: -1.4 + 10.89 = 9.49 10.89 + 6.6x + x2 = 9.49 Factor a perfect square on the left side: (x + 3.3)(x + 3.3) = 9.49 Calculate the square root of the right side: 3.08058436 Break this problem into two subproblems by setting (x + 3.3) equal to 3.08058436 and -3.08058436.Subproblem 1
x + 3.3 = 3.08058436 Simplifying x + 3.3 = 3.08058436 Reorder the terms: 3.3 + x = 3.08058436 Solving 3.3 + x = 3.08058436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + x = 3.08058436 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = 3.08058436 + -3.3 x = 3.08058436 + -3.3 Combine like terms: 3.08058436 + -3.3 = -0.21941564 x = -0.21941564 Simplifying x = -0.21941564Subproblem 2
x + 3.3 = -3.08058436 Simplifying x + 3.3 = -3.08058436 Reorder the terms: 3.3 + x = -3.08058436 Solving 3.3 + x = -3.08058436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + x = -3.08058436 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = -3.08058436 + -3.3 x = -3.08058436 + -3.3 Combine like terms: -3.08058436 + -3.3 = -6.38058436 x = -6.38058436 Simplifying x = -6.38058436Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.21941564, -6.38058436}Solution
x = {0, -0.21941564, -6.38058436}
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