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Simplifying 3x(14x + -15) = -72 Reorder the terms: 3x(-15 + 14x) = -72 (-15 * 3x + 14x * 3x) = -72 (-45x + 42x2) = -72 Solving -45x + 42x2 = -72 Solving for variable 'x'. Reorder the terms: 72 + -45x + 42x2 = -72 + 72 Combine like terms: -72 + 72 = 0 72 + -45x + 42x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(24 + -15x + 14x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(24 + -15x + 14x2)' equal to zero and attempt to solve: Simplifying 24 + -15x + 14x2 = 0 Solving 24 + -15x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 1.714285714 + -1.071428571x + x2 = 0 Move the constant term to the right: Add '-1.714285714' to each side of the equation. 1.714285714 + -1.071428571x + -1.714285714 + x2 = 0 + -1.714285714 Reorder the terms: 1.714285714 + -1.714285714 + -1.071428571x + x2 = 0 + -1.714285714 Combine like terms: 1.714285714 + -1.714285714 = 0.000000000 0.000000000 + -1.071428571x + x2 = 0 + -1.714285714 -1.071428571x + x2 = 0 + -1.714285714 Combine like terms: 0 + -1.714285714 = -1.714285714 -1.071428571x + x2 = -1.714285714 The x term is -1.071428571x. Take half its coefficient (-0.5357142855). Square it (0.2869897957) and add it to both sides. Add '0.2869897957' to each side of the equation. -1.071428571x + 0.2869897957 + x2 = -1.714285714 + 0.2869897957 Reorder the terms: 0.2869897957 + -1.071428571x + x2 = -1.714285714 + 0.2869897957 Combine like terms: -1.714285714 + 0.2869897957 = -1.4272959183 0.2869897957 + -1.071428571x + x2 = -1.4272959183 Factor a perfect square on the left side: (x + -0.5357142855)(x + -0.5357142855) = -1.4272959183 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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