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Simplifying 7x3 + -6x2 + 4x * 2x2 + -3x = 0 Reorder the terms for easier multiplication: 7x3 + -6x2 + 4 * 2x * x2 + -3x = 0 Multiply 4 * 2 7x3 + -6x2 + 8x * x2 + -3x = 0 Multiply x * x2 7x3 + -6x2 + 8x3 + -3x = 0 Reorder the terms: -3x + -6x2 + 7x3 + 8x3 = 0 Combine like terms: 7x3 + 8x3 = 15x3 -3x + -6x2 + 15x3 = 0 Solving -3x + -6x2 + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-1 + -2x + 5x2) = 0 Ignore the factor 3.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 '(-1 + -2x + 5x2)' equal to zero and attempt to solve: Simplifying -1 + -2x + 5x2 = 0 Solving -1 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.4x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.4x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.4x + x2 = 0 + 0.2 -0.4x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.4x + x2 = 0.2 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.2 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.2 + 0.04 Combine like terms: 0.2 + 0.04 = 0.24 0.04 + -0.4x + x2 = 0.24 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + -0.2) equal to 0.489897949 and -0.489897949.Subproblem 1
x + -0.2 = 0.489897949 Simplifying x + -0.2 = 0.489897949 Reorder the terms: -0.2 + x = 0.489897949 Solving -0.2 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.489897949 + 0.2 x = 0.489897949 + 0.2 Combine like terms: 0.489897949 + 0.2 = 0.689897949 x = 0.689897949 Simplifying x = 0.689897949Subproblem 2
x + -0.2 = -0.489897949 Simplifying x + -0.2 = -0.489897949 Reorder the terms: -0.2 + x = -0.489897949 Solving -0.2 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.489897949 + 0.2 x = -0.489897949 + 0.2 Combine like terms: -0.489897949 + 0.2 = -0.289897949 x = -0.289897949 Simplifying x = -0.289897949Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.689897949, -0.289897949}Solution
x = {0, 0.689897949, -0.289897949}
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