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Simplifying 300x2 + -750x + 1.5625 = -625 + 1.5625 Reorder the terms: 1.5625 + -750x + 300x2 = -625 + 1.5625 Combine like terms: -625 + 1.5625 = -623.4375 1.5625 + -750x + 300x2 = -623.4375 Solving 1.5625 + -750x + 300x2 = -623.4375 Solving for variable 'x'. Reorder the terms: 1.5625 + 623.4375 + -750x + 300x2 = -623.4375 + 623.4375 Combine like terms: 1.5625 + 623.4375 = 625 625 + -750x + 300x2 = -623.4375 + 623.4375 Combine like terms: -623.4375 + 623.4375 = 0.0000 625 + -750x + 300x2 = 0.0000 Factor out the Greatest Common Factor (GCF), '25'. 25(25 + -30x + 12x2) = 0.0000 Ignore the factor 25.Subproblem 1
Set the factor '(25 + -30x + 12x2)' equal to zero and attempt to solve: Simplifying 25 + -30x + 12x2 = 0 Solving 25 + -30x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 2.083333333 + -2.5x + x2 = 0 Move the constant term to the right: Add '-2.083333333' to each side of the equation. 2.083333333 + -2.5x + -2.083333333 + x2 = 0 + -2.083333333 Reorder the terms: 2.083333333 + -2.083333333 + -2.5x + x2 = 0 + -2.083333333 Combine like terms: 2.083333333 + -2.083333333 = 0.000000000 0.000000000 + -2.5x + x2 = 0 + -2.083333333 -2.5x + x2 = 0 + -2.083333333 Combine like terms: 0 + -2.083333333 = -2.083333333 -2.5x + x2 = -2.083333333 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -2.083333333 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -2.083333333 + 1.5625 Combine like terms: -2.083333333 + 1.5625 = -0.520833333 1.5625 + -2.5x + x2 = -0.520833333 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -0.520833333 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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