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Simplifying 10x2 + -35x = -40 Reorder the terms: -35x + 10x2 = -40 Solving -35x + 10x2 = -40 Solving for variable 'x'. Reorder the terms: 40 + -35x + 10x2 = -40 + 40 Combine like terms: -40 + 40 = 0 40 + -35x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(8 + -7x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(8 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying 8 + -7x + 2x2 = 0 Solving 8 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -3.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -3.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3.5x + x2 = 0 + -4 -3.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3.5x + x2 = -4 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -4 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -4 + 3.0625 Combine like terms: -4 + 3.0625 = -0.9375 3.0625 + -3.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -0.9375 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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