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Simplifying 24x + 36 = -10x2 + -160 Reorder the terms: 36 + 24x = -10x2 + -160 Reorder the terms: 36 + 24x = -160 + -10x2 Solving 36 + 24x = -160 + -10x2 Solving for variable 'x'. Reorder the terms: 36 + 160 + 24x + 10x2 = -160 + -10x2 + 160 + 10x2 Combine like terms: 36 + 160 = 196 196 + 24x + 10x2 = -160 + -10x2 + 160 + 10x2 Reorder the terms: 196 + 24x + 10x2 = -160 + 160 + -10x2 + 10x2 Combine like terms: -160 + 160 = 0 196 + 24x + 10x2 = 0 + -10x2 + 10x2 196 + 24x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 196 + 24x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(98 + 12x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(98 + 12x + 5x2)' equal to zero and attempt to solve: Simplifying 98 + 12x + 5x2 = 0 Solving 98 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 19.6 + 2.4x + x2 = 0 Move the constant term to the right: Add '-19.6' to each side of the equation. 19.6 + 2.4x + -19.6 + x2 = 0 + -19.6 Reorder the terms: 19.6 + -19.6 + 2.4x + x2 = 0 + -19.6 Combine like terms: 19.6 + -19.6 = 0.0 0.0 + 2.4x + x2 = 0 + -19.6 2.4x + x2 = 0 + -19.6 Combine like terms: 0 + -19.6 = -19.6 2.4x + x2 = -19.6 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = -19.6 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = -19.6 + 1.44 Combine like terms: -19.6 + 1.44 = -18.16 1.44 + 2.4x + x2 = -18.16 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = -18.16 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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