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Simplifying 10x2 + 18x + 28 = 0 Reorder the terms: 28 + 18x + 10x2 = 0 Solving 28 + 18x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 9x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + 9x + 5x2)' equal to zero and attempt to solve: Simplifying 14 + 9x + 5x2 = 0 Solving 14 + 9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + 1.8x + x2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + 1.8x + -2.8 + x2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + 1.8x + x2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 1.8x + x2 = 0 + -2.8 1.8x + x2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 1.8x + x2 = -2.8 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = -2.8 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = -2.8 + 0.81 Combine like terms: -2.8 + 0.81 = -1.99 0.81 + 1.8x + x2 = -1.99 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = -1.99 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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