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Simplifying 10x2 + 32x + 30 = 0 Reorder the terms: 30 + 32x + 10x2 = 0 Solving 30 + 32x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 16x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 16x + 5x2)' equal to zero and attempt to solve: Simplifying 15 + 16x + 5x2 = 0 Solving 15 + 16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + 3.2x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3.2x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3.2x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3.2x + x2 = 0 + -3 3.2x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3.2x + x2 = -3 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = -3 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = -3 + 2.56 Combine like terms: -3 + 2.56 = -0.44 2.56 + 3.2x + x2 = -0.44 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = -0.44 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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