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Simplifying 4x(7x2 + 3x + -6) = 0 Reorder the terms: 4x(-6 + 3x + 7x2) = 0 (-6 * 4x + 3x * 4x + 7x2 * 4x) = 0 (-24x + 12x2 + 28x3) = 0 Solving -24x + 12x2 + 28x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-6 + 3x + 7x2) = 0 Ignore the factor 4.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 '(-6 + 3x + 7x2)' equal to zero and attempt to solve: Simplifying -6 + 3x + 7x2 = 0 Solving -6 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 0.4285714286x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 0.4285714286x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 0.4285714286x + x2 = 0 + 0.8571428571 0.4285714286x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 0.4285714286x + x2 = 0.8571428571 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 0.8571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 0.8571428571 + 0.04591836735 Combine like terms: 0.8571428571 + 0.04591836735 = 0.90306122445 0.04591836735 + 0.4285714286x + x2 = 0.90306122445 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 0.90306122445 Calculate the square root of the right side: 0.950295335 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 0.950295335 and -0.950295335.Subproblem 1
x + 0.2142857143 = 0.950295335 Simplifying x + 0.2142857143 = 0.950295335 Reorder the terms: 0.2142857143 + x = 0.950295335 Solving 0.2142857143 + x = 0.950295335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 0.950295335 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 0.950295335 + -0.2142857143 x = 0.950295335 + -0.2142857143 Combine like terms: 0.950295335 + -0.2142857143 = 0.7360096207 x = 0.7360096207 Simplifying x = 0.7360096207Subproblem 2
x + 0.2142857143 = -0.950295335 Simplifying x + 0.2142857143 = -0.950295335 Reorder the terms: 0.2142857143 + x = -0.950295335 Solving 0.2142857143 + x = -0.950295335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -0.950295335 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -0.950295335 + -0.2142857143 x = -0.950295335 + -0.2142857143 Combine like terms: -0.950295335 + -0.2142857143 = -1.1645810493 x = -1.1645810493 Simplifying x = -1.1645810493Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7360096207, -1.1645810493}Solution
x = {0, 0.7360096207, -1.1645810493}
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