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Simplifying x = 16x2 + 40x + 560 Reorder the terms: x = 560 + 40x + 16x2 Solving x = 560 + 40x + 16x2 Solving for variable 'x'. Reorder the terms: -560 + x + -40x + -16x2 = 560 + 40x + 16x2 + -560 + -40x + -16x2 Combine like terms: x + -40x = -39x -560 + -39x + -16x2 = 560 + 40x + 16x2 + -560 + -40x + -16x2 Reorder the terms: -560 + -39x + -16x2 = 560 + -560 + 40x + -40x + 16x2 + -16x2 Combine like terms: 560 + -560 = 0 -560 + -39x + -16x2 = 0 + 40x + -40x + 16x2 + -16x2 -560 + -39x + -16x2 = 40x + -40x + 16x2 + -16x2 Combine like terms: 40x + -40x = 0 -560 + -39x + -16x2 = 0 + 16x2 + -16x2 -560 + -39x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -560 + -39x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(560 + 39x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(560 + 39x + 16x2)' equal to zero and attempt to solve: Simplifying 560 + 39x + 16x2 = 0 Solving 560 + 39x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 35 + 2.4375x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + 2.4375x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + 2.4375x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 2.4375x + x2 = 0 + -35 2.4375x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 2.4375x + x2 = -35 The x term is 2.4375x. Take half its coefficient (1.21875). Square it (1.485351563) and add it to both sides. Add '1.485351563' to each side of the equation. 2.4375x + 1.485351563 + x2 = -35 + 1.485351563 Reorder the terms: 1.485351563 + 2.4375x + x2 = -35 + 1.485351563 Combine like terms: -35 + 1.485351563 = -33.514648437 1.485351563 + 2.4375x + x2 = -33.514648437 Factor a perfect square on the left side: (x + 1.21875)(x + 1.21875) = -33.514648437 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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