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Simplifying -0.4x(10x + -25) = 8x + 4 Reorder the terms: -0.4x(-25 + 10x) = 8x + 4 (-25 * -0.4x + 10x * -0.4x) = 8x + 4 (10x + -4x2) = 8x + 4 Reorder the terms: 10x + -4x2 = 4 + 8x Solving 10x + -4x2 = 4 + 8x Solving for variable 'x'. Reorder the terms: -4 + 10x + -8x + -4x2 = 4 + 8x + -4 + -8x Combine like terms: 10x + -8x = 2x -4 + 2x + -4x2 = 4 + 8x + -4 + -8x Reorder the terms: -4 + 2x + -4x2 = 4 + -4 + 8x + -8x Combine like terms: 4 + -4 = 0 -4 + 2x + -4x2 = 0 + 8x + -8x -4 + 2x + -4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -4 + 2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + x + -2x2)' equal to zero and attempt to solve: Simplifying -2 + x + -2x2 = 0 Solving -2 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1 + -0.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -0.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.5x + x2 = 0 + -1 -0.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.5x + x2 = -1 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -0.5x + x2 = -0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.75 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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