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Simplifying 5(1 + -1x) * 2x = 15 Reorder the terms for easier multiplication: 5 * 2x(1 + -1x) = 15 Multiply 5 * 2 10x(1 + -1x) = 15 (1 * 10x + -1x * 10x) = 15 (10x + -10x2) = 15 Solving 10x + -10x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 10x + -10x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 10x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + 2x + -2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + 2x + -2x2)' equal to zero and attempt to solve: Simplifying -3 + 2x + -2x2 = 0 Solving -3 + 2x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -1x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -1x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -1x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -1x + x2 = 0 + -1.5 -1x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -1x + x2 = -1.5 The x term is -1x. 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. -1x + 0.25 + x2 = -1.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -1.5 + 0.25 Combine like terms: -1.5 + 0.25 = -1.25 0.25 + -1x + x2 = -1.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -1.25 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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