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Simplifying (2x3 + -10x2 + 2x + -9) + -7x3 + -10x2 + -5x + 9 = 0 Reorder the terms: (-9 + 2x + -10x2 + 2x3) + -7x3 + -10x2 + -5x + 9 = 0 Remove parenthesis around (-9 + 2x + -10x2 + 2x3) -9 + 2x + -10x2 + 2x3 + -7x3 + -10x2 + -5x + 9 = 0 Reorder the terms: -9 + 9 + 2x + -5x + -10x2 + -10x2 + 2x3 + -7x3 = 0 Combine like terms: -9 + 9 = 0 0 + 2x + -5x + -10x2 + -10x2 + 2x3 + -7x3 = 0 2x + -5x + -10x2 + -10x2 + 2x3 + -7x3 = 0 Combine like terms: 2x + -5x = -3x -3x + -10x2 + -10x2 + 2x3 + -7x3 = 0 Combine like terms: -10x2 + -10x2 = -20x2 -3x + -20x2 + 2x3 + -7x3 = 0 Combine like terms: 2x3 + -7x3 = -5x3 -3x + -20x2 + -5x3 = 0 Solving -3x + -20x2 + -5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1x'. -1x(3 + 20x + 5x2) = 0 Ignore the factor -1.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 '(3 + 20x + 5x2)' equal to zero and attempt to solve: Simplifying 3 + 20x + 5x2 = 0 Solving 3 + 20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 4x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 4x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 4x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 4x + x2 = 0 + -0.6 4x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 4x + x2 = -0.6 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -0.6 + 4 Reorder the terms: 4 + 4x + x2 = -0.6 + 4 Combine like terms: -0.6 + 4 = 3.4 4 + 4x + x2 = 3.4 Factor a perfect square on the left side: (x + 2)(x + 2) = 3.4 Calculate the square root of the right side: 1.843908891 Break this problem into two subproblems by setting (x + 2) equal to 1.843908891 and -1.843908891.Subproblem 1
x + 2 = 1.843908891 Simplifying x + 2 = 1.843908891 Reorder the terms: 2 + x = 1.843908891 Solving 2 + x = 1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.843908891 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.843908891 + -2 x = 1.843908891 + -2 Combine like terms: 1.843908891 + -2 = -0.156091109 x = -0.156091109 Simplifying x = -0.156091109Subproblem 2
x + 2 = -1.843908891 Simplifying x + 2 = -1.843908891 Reorder the terms: 2 + x = -1.843908891 Solving 2 + x = -1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.843908891 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.843908891 + -2 x = -1.843908891 + -2 Combine like terms: -1.843908891 + -2 = -3.843908891 x = -3.843908891 Simplifying x = -3.843908891Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.156091109, -3.843908891}Solution
x = {0, -0.156091109, -3.843908891}
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