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Simplifying -2x3(5x2 + -3x + -7) = 0 Reorder the terms: -2x3(-7 + -3x + 5x2) = 0 (-7 * -2x3 + -3x * -2x3 + 5x2 * -2x3) = 0 (14x3 + 6x4 + -10x5) = 0 Solving 14x3 + 6x4 + -10x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x3'. 2x3(7 + 3x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(7 + 3x + -5x2)' equal to zero and attempt to solve: Simplifying 7 + 3x + -5x2 = 0 Solving 7 + 3x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.4 + -0.6x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.6x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.6x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.6x + x2 = 0 + 1.4 -0.6x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.6x + x2 = 1.4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 1.4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1.4 + 0.09 Combine like terms: 1.4 + 0.09 = 1.49 0.09 + -0.6x + x2 = 1.49 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (x + -0.3) equal to 1.220655562 and -1.220655562.Subproblem 1
x + -0.3 = 1.220655562 Simplifying x + -0.3 = 1.220655562 Reorder the terms: -0.3 + x = 1.220655562 Solving -0.3 + x = 1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.220655562 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.220655562 + 0.3 x = 1.220655562 + 0.3 Combine like terms: 1.220655562 + 0.3 = 1.520655562 x = 1.520655562 Simplifying x = 1.520655562Subproblem 2
x + -0.3 = -1.220655562 Simplifying x + -0.3 = -1.220655562 Reorder the terms: -0.3 + x = -1.220655562 Solving -0.3 + x = -1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.220655562 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.220655562 + 0.3 x = -1.220655562 + 0.3 Combine like terms: -1.220655562 + 0.3 = -0.920655562 x = -0.920655562 Simplifying x = -0.920655562Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.520655562, -0.920655562}Solution
x = {1.520655562, -0.920655562}
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