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Simplifying 4x + 1 = 25x2 + 30x + 9 Reorder the terms: 1 + 4x = 25x2 + 30x + 9 Reorder the terms: 1 + 4x = 9 + 30x + 25x2 Solving 1 + 4x = 9 + 30x + 25x2 Solving for variable 'x'. Reorder the terms: 1 + -9 + 4x + -30x + -25x2 = 9 + 30x + 25x2 + -9 + -30x + -25x2 Combine like terms: 1 + -9 = -8 -8 + 4x + -30x + -25x2 = 9 + 30x + 25x2 + -9 + -30x + -25x2 Combine like terms: 4x + -30x = -26x -8 + -26x + -25x2 = 9 + 30x + 25x2 + -9 + -30x + -25x2 Reorder the terms: -8 + -26x + -25x2 = 9 + -9 + 30x + -30x + 25x2 + -25x2 Combine like terms: 9 + -9 = 0 -8 + -26x + -25x2 = 0 + 30x + -30x + 25x2 + -25x2 -8 + -26x + -25x2 = 30x + -30x + 25x2 + -25x2 Combine like terms: 30x + -30x = 0 -8 + -26x + -25x2 = 0 + 25x2 + -25x2 -8 + -26x + -25x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 -8 + -26x + -25x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 26x + 25x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 26x + 25x2)' equal to zero and attempt to solve: Simplifying 8 + 26x + 25x2 = 0 Solving 8 + 26x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.32 + 1.04x + x2 = 0 Move the constant term to the right: Add '-0.32' to each side of the equation. 0.32 + 1.04x + -0.32 + x2 = 0 + -0.32 Reorder the terms: 0.32 + -0.32 + 1.04x + x2 = 0 + -0.32 Combine like terms: 0.32 + -0.32 = 0.00 0.00 + 1.04x + x2 = 0 + -0.32 1.04x + x2 = 0 + -0.32 Combine like terms: 0 + -0.32 = -0.32 1.04x + x2 = -0.32 The x term is 1.04x. Take half its coefficient (0.52). Square it (0.2704) and add it to both sides. Add '0.2704' to each side of the equation. 1.04x + 0.2704 + x2 = -0.32 + 0.2704 Reorder the terms: 0.2704 + 1.04x + x2 = -0.32 + 0.2704 Combine like terms: -0.32 + 0.2704 = -0.0496 0.2704 + 1.04x + x2 = -0.0496 Factor a perfect square on the left side: (x + 0.52)(x + 0.52) = -0.0496 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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