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Simplifying 5(-4x + 2) * 5x + -3 = 257 Reorder the terms: 5(2 + -4x) * 5x + -3 = 257 Reorder the terms for easier multiplication: 5 * 5x(2 + -4x) + -3 = 257 Multiply 5 * 5 25x(2 + -4x) + -3 = 257 (2 * 25x + -4x * 25x) + -3 = 257 (50x + -100x2) + -3 = 257 Reorder the terms: -3 + 50x + -100x2 = 257 Solving -3 + 50x + -100x2 = 257 Solving for variable 'x'. Reorder the terms: -3 + -257 + 50x + -100x2 = 257 + -257 Combine like terms: -3 + -257 = -260 -260 + 50x + -100x2 = 257 + -257 Combine like terms: 257 + -257 = 0 -260 + 50x + -100x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-26 + 5x + -10x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-26 + 5x + -10x2)' equal to zero and attempt to solve: Simplifying -26 + 5x + -10x2 = 0 Solving -26 + 5x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 2.6 + -0.5x + x2 = 0.0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + -0.5x + -2.6 + x2 = 0.0 + -2.6 Reorder the terms: 2.6 + -2.6 + -0.5x + x2 = 0.0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + -0.5x + x2 = 0.0 + -2.6 -0.5x + x2 = 0.0 + -2.6 Combine like terms: 0.0 + -2.6 = -2.6 -0.5x + x2 = -2.6 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 = -2.6 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -2.6 + 0.0625 Combine like terms: -2.6 + 0.0625 = -2.5375 0.0625 + -0.5x + x2 = -2.5375 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -2.5375 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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