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Simplifying 4x2 + -5(9 + x2) + -9x2 + 12x + 4 = 35 4x2 + (9 * -5 + x2 * -5) + -9x2 + 12x + 4 = 35 4x2 + (-45 + -5x2) + -9x2 + 12x + 4 = 35 Reorder the terms: -45 + 4 + 12x + 4x2 + -5x2 + -9x2 = 35 Combine like terms: -45 + 4 = -41 -41 + 12x + 4x2 + -5x2 + -9x2 = 35 Combine like terms: 4x2 + -5x2 = -1x2 -41 + 12x + -1x2 + -9x2 = 35 Combine like terms: -1x2 + -9x2 = -10x2 -41 + 12x + -10x2 = 35 Solving -41 + 12x + -10x2 = 35 Solving for variable 'x'. Reorder the terms: -41 + -35 + 12x + -10x2 = 35 + -35 Combine like terms: -41 + -35 = -76 -76 + 12x + -10x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -76 + 12x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-38 + 6x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-38 + 6x + -5x2)' equal to zero and attempt to solve: Simplifying -38 + 6x + -5x2 = 0 Solving -38 + 6x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 7.6 + -1.2x + x2 = 0 Move the constant term to the right: Add '-7.6' to each side of the equation. 7.6 + -1.2x + -7.6 + x2 = 0 + -7.6 Reorder the terms: 7.6 + -7.6 + -1.2x + x2 = 0 + -7.6 Combine like terms: 7.6 + -7.6 = 0.0 0.0 + -1.2x + x2 = 0 + -7.6 -1.2x + x2 = 0 + -7.6 Combine like terms: 0 + -7.6 = -7.6 -1.2x + x2 = -7.6 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -7.6 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -7.6 + 0.36 Combine like terms: -7.6 + 0.36 = -7.24 0.36 + -1.2x + x2 = -7.24 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = -7.24 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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