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Simplifying 10x(7x2 + 9x + 6) = 0 Reorder the terms: 10x(6 + 9x + 7x2) = 0 (6 * 10x + 9x * 10x + 7x2 * 10x) = 0 (60x + 90x2 + 70x3) = 0 Solving 60x + 90x2 + 70x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x'. 10x(6 + 9x + 7x2) = 0 Ignore the factor 10.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 + 9x + 7x2)' equal to zero and attempt to solve: Simplifying 6 + 9x + 7x2 = 0 Solving 6 + 9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 1.285714286x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 1.285714286x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 1.285714286x + x2 = 0 + -0.8571428571 1.285714286x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 1.285714286x + x2 = -0.8571428571 The x term is 1.285714286x. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286x + 0.4132653063 + x2 = -0.8571428571 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = -0.8571428571 + 0.4132653063 Combine like terms: -0.8571428571 + 0.4132653063 = -0.4438775508 0.4132653063 + 1.285714286x + x2 = -0.4438775508 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = -0.4438775508 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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