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Simplifying 5x + 5x + -5x(2x + 3) = 1 Reorder the terms: 5x + 5x + -5x(3 + 2x) = 1 5x + 5x + (3 * -5x + 2x * -5x) = 1 5x + 5x + (-15x + -10x2) = 1 Combine like terms: 5x + 5x = 10x 10x + -15x + -10x2 = 1 Combine like terms: 10x + -15x = -5x -5x + -10x2 = 1 Solving -5x + -10x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -5x + -10x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -5x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 5x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 5x + 10x2)' equal to zero and attempt to solve: Simplifying 1 + 5x + 10x2 = 0 Solving 1 + 5x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.1 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 0.5x + -0.1 + x2 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + 0.5x + x2 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 0.5x + x2 = 0.0 + -0.1 0.5x + x2 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 0.5x + x2 = -0.1 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -0.1 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.1 + 0.0625 Combine like terms: -0.1 + 0.0625 = -0.0375 0.0625 + 0.5x + x2 = -0.0375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -0.0375 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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