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Simplifying 4x2 + -25 = 9x2 + 30x + 25 Reorder the terms: -25 + 4x2 = 9x2 + 30x + 25 Reorder the terms: -25 + 4x2 = 25 + 30x + 9x2 Solving -25 + 4x2 = 25 + 30x + 9x2 Solving for variable 'x'. Reorder the terms: -25 + -25 + -30x + 4x2 + -9x2 = 25 + 30x + 9x2 + -25 + -30x + -9x2 Combine like terms: -25 + -25 = -50 -50 + -30x + 4x2 + -9x2 = 25 + 30x + 9x2 + -25 + -30x + -9x2 Combine like terms: 4x2 + -9x2 = -5x2 -50 + -30x + -5x2 = 25 + 30x + 9x2 + -25 + -30x + -9x2 Reorder the terms: -50 + -30x + -5x2 = 25 + -25 + 30x + -30x + 9x2 + -9x2 Combine like terms: 25 + -25 = 0 -50 + -30x + -5x2 = 0 + 30x + -30x + 9x2 + -9x2 -50 + -30x + -5x2 = 30x + -30x + 9x2 + -9x2 Combine like terms: 30x + -30x = 0 -50 + -30x + -5x2 = 0 + 9x2 + -9x2 -50 + -30x + -5x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -50 + -30x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-5'. -5(10 + 6x + x2) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(10 + 6x + x2)' equal to zero and attempt to solve: Simplifying 10 + 6x + x2 = 0 Solving 10 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 6x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 6x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 6x + x2 = 0 + -10 6x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 6x + x2 = -10 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -10 + 9 Reorder the terms: 9 + 6x + x2 = -10 + 9 Combine like terms: -10 + 9 = -1 9 + 6x + x2 = -1 Factor a perfect square on the left side: (x + 3)(x + 3) = -1 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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