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Simplifying 6 + -9x(6 + 14x) = 824 6 + (6 * -9x + 14x * -9x) = 824 6 + (-54x + -126x2) = 824 Solving 6 + -54x + -126x2 = 824 Solving for variable 'x'. Reorder the terms: 6 + -824 + -54x + -126x2 = 824 + -824 Combine like terms: 6 + -824 = -818 -818 + -54x + -126x2 = 824 + -824 Combine like terms: 824 + -824 = 0 -818 + -54x + -126x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(409 + 27x + 63x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(409 + 27x + 63x2)' equal to zero and attempt to solve: Simplifying 409 + 27x + 63x2 = 0 Solving 409 + 27x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. 6.492063492 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '-6.492063492' to each side of the equation. 6.492063492 + 0.4285714286x + -6.492063492 + x2 = 0 + -6.492063492 Reorder the terms: 6.492063492 + -6.492063492 + 0.4285714286x + x2 = 0 + -6.492063492 Combine like terms: 6.492063492 + -6.492063492 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + -6.492063492 0.4285714286x + x2 = 0 + -6.492063492 Combine like terms: 0 + -6.492063492 = -6.492063492 0.4285714286x + x2 = -6.492063492 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 = -6.492063492 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = -6.492063492 + 0.04591836735 Combine like terms: -6.492063492 + 0.04591836735 = -6.44614512465 0.04591836735 + 0.4285714286x + x2 = -6.44614512465 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = -6.44614512465 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. The solution to this equation could not be determined.
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