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Simplifying 15x * 15x + -18x = -24 Reorder the terms for easier multiplication: 15 * 15x * x + -18x = -24 Multiply 15 * 15 225x * x + -18x = -24 Multiply x * x 225x2 + -18x = -24 Reorder the terms: -18x + 225x2 = -24 Solving -18x + 225x2 = -24 Solving for variable 'x'. Reorder the terms: 24 + -18x + 225x2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + -18x + 225x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + -6x + 75x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -6x + 75x2)' equal to zero and attempt to solve: Simplifying 8 + -6x + 75x2 = 0 Solving 8 + -6x + 75x2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. 0.1066666667 + -0.08x + x2 = 0 Move the constant term to the right: Add '-0.1066666667' to each side of the equation. 0.1066666667 + -0.08x + -0.1066666667 + x2 = 0 + -0.1066666667 Reorder the terms: 0.1066666667 + -0.1066666667 + -0.08x + x2 = 0 + -0.1066666667 Combine like terms: 0.1066666667 + -0.1066666667 = 0.0000000000 0.0000000000 + -0.08x + x2 = 0 + -0.1066666667 -0.08x + x2 = 0 + -0.1066666667 Combine like terms: 0 + -0.1066666667 = -0.1066666667 -0.08x + x2 = -0.1066666667 The x term is -0.08x. Take half its coefficient (-0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. -0.08x + 0.0016 + x2 = -0.1066666667 + 0.0016 Reorder the terms: 0.0016 + -0.08x + x2 = -0.1066666667 + 0.0016 Combine like terms: -0.1066666667 + 0.0016 = -0.1050666667 0.0016 + -0.08x + x2 = -0.1050666667 Factor a perfect square on the left side: (x + -0.04)(x + -0.04) = -0.1050666667 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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