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Simplifying 19x(4x + -2) = 6(-4x + -12) Reorder the terms: 19x(-2 + 4x) = 6(-4x + -12) (-2 * 19x + 4x * 19x) = 6(-4x + -12) (-38x + 76x2) = 6(-4x + -12) Reorder the terms: -38x + 76x2 = 6(-12 + -4x) -38x + 76x2 = (-12 * 6 + -4x * 6) -38x + 76x2 = (-72 + -24x) Solving -38x + 76x2 = -72 + -24x Solving for variable 'x'. Reorder the terms: 72 + -38x + 24x + 76x2 = -72 + -24x + 72 + 24x Combine like terms: -38x + 24x = -14x 72 + -14x + 76x2 = -72 + -24x + 72 + 24x Reorder the terms: 72 + -14x + 76x2 = -72 + 72 + -24x + 24x Combine like terms: -72 + 72 = 0 72 + -14x + 76x2 = 0 + -24x + 24x 72 + -14x + 76x2 = -24x + 24x Combine like terms: -24x + 24x = 0 72 + -14x + 76x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(36 + -7x + 38x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + -7x + 38x2)' equal to zero and attempt to solve: Simplifying 36 + -7x + 38x2 = 0 Solving 36 + -7x + 38x2 = 0 Begin completing the square. Divide all terms by 38 the coefficient of the squared term: Divide each side by '38'. 0.9473684211 + -0.1842105263x + x2 = 0 Move the constant term to the right: Add '-0.9473684211' to each side of the equation. 0.9473684211 + -0.1842105263x + -0.9473684211 + x2 = 0 + -0.9473684211 Reorder the terms: 0.9473684211 + -0.9473684211 + -0.1842105263x + x2 = 0 + -0.9473684211 Combine like terms: 0.9473684211 + -0.9473684211 = 0.0000000000 0.0000000000 + -0.1842105263x + x2 = 0 + -0.9473684211 -0.1842105263x + x2 = 0 + -0.9473684211 Combine like terms: 0 + -0.9473684211 = -0.9473684211 -0.1842105263x + x2 = -0.9473684211 The x term is -0.1842105263x. Take half its coefficient (-0.09210526315). Square it (0.008483379500) and add it to both sides. Add '0.008483379500' to each side of the equation. -0.1842105263x + 0.008483379500 + x2 = -0.9473684211 + 0.008483379500 Reorder the terms: 0.008483379500 + -0.1842105263x + x2 = -0.9473684211 + 0.008483379500 Combine like terms: -0.9473684211 + 0.008483379500 = -0.9388850416 0.008483379500 + -0.1842105263x + x2 = -0.9388850416 Factor a perfect square on the left side: (x + -0.09210526315)(x + -0.09210526315) = -0.9388850416 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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