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Simplifying 5(25x2 + 35x + 49) = 0 Reorder the terms: 5(49 + 35x + 25x2) = 0 (49 * 5 + 35x * 5 + 25x2 * 5) = 0 (245 + 175x + 125x2) = 0 Solving 245 + 175x + 125x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(49 + 35x + 25x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(49 + 35x + 25x2)' equal to zero and attempt to solve: Simplifying 49 + 35x + 25x2 = 0 Solving 49 + 35x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.96 + 1.4x + x2 = 0 Move the constant term to the right: Add '-1.96' to each side of the equation. 1.96 + 1.4x + -1.96 + x2 = 0 + -1.96 Reorder the terms: 1.96 + -1.96 + 1.4x + x2 = 0 + -1.96 Combine like terms: 1.96 + -1.96 = 0.00 0.00 + 1.4x + x2 = 0 + -1.96 1.4x + x2 = 0 + -1.96 Combine like terms: 0 + -1.96 = -1.96 1.4x + x2 = -1.96 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -1.96 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -1.96 + 0.49 Combine like terms: -1.96 + 0.49 = -1.47 0.49 + 1.4x + x2 = -1.47 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = -1.47 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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