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Simplifying 6x2 + 6x = 96x2 + 24 + -16x + -4 Reorder the terms: 6x + 6x2 = 96x2 + 24 + -16x + -4 Reorder the terms: 6x + 6x2 = 24 + -4 + -16x + 96x2 Combine like terms: 24 + -4 = 20 6x + 6x2 = 20 + -16x + 96x2 Solving 6x + 6x2 = 20 + -16x + 96x2 Solving for variable 'x'. Reorder the terms: -20 + 6x + 16x + 6x2 + -96x2 = 20 + -16x + 96x2 + -20 + 16x + -96x2 Combine like terms: 6x + 16x = 22x -20 + 22x + 6x2 + -96x2 = 20 + -16x + 96x2 + -20 + 16x + -96x2 Combine like terms: 6x2 + -96x2 = -90x2 -20 + 22x + -90x2 = 20 + -16x + 96x2 + -20 + 16x + -96x2 Reorder the terms: -20 + 22x + -90x2 = 20 + -20 + -16x + 16x + 96x2 + -96x2 Combine like terms: 20 + -20 = 0 -20 + 22x + -90x2 = 0 + -16x + 16x + 96x2 + -96x2 -20 + 22x + -90x2 = -16x + 16x + 96x2 + -96x2 Combine like terms: -16x + 16x = 0 -20 + 22x + -90x2 = 0 + 96x2 + -96x2 -20 + 22x + -90x2 = 96x2 + -96x2 Combine like terms: 96x2 + -96x2 = 0 -20 + 22x + -90x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 11x + -45x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 11x + -45x2)' equal to zero and attempt to solve: Simplifying -10 + 11x + -45x2 = 0 Solving -10 + 11x + -45x2 = 0 Begin completing the square. Divide all terms by -45 the coefficient of the squared term: Divide each side by '-45'. 0.2222222222 + -0.2444444444x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2444444444x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -0.2444444444x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -0.2444444444x + x2 = 0 + -0.2222222222 -0.2444444444x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -0.2444444444x + x2 = -0.2222222222 The x term is -0.2444444444x. Take half its coefficient (-0.1222222222). Square it (0.01493827160) and add it to both sides. Add '0.01493827160' to each side of the equation. -0.2444444444x + 0.01493827160 + x2 = -0.2222222222 + 0.01493827160 Reorder the terms: 0.01493827160 + -0.2444444444x + x2 = -0.2222222222 + 0.01493827160 Combine like terms: -0.2222222222 + 0.01493827160 = -0.2072839506 0.01493827160 + -0.2444444444x + x2 = -0.2072839506 Factor a perfect square on the left side: (x + -0.1222222222)(x + -0.1222222222) = -0.2072839506 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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