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Simplifying 10x2 + -14x + 8 = 0 Reorder the terms: 8 + -14x + 10x2 = 0 Solving 8 + -14x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -7x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -7x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + -7x + 5x2 = 0 Solving 4 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -1.4x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -1.4x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -1.4x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -1.4x + x2 = 0 + -0.8 -1.4x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -1.4x + x2 = -0.8 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 = -0.8 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -0.8 + 0.49 Combine like terms: -0.8 + 0.49 = -0.31 0.49 + -1.4x + x2 = -0.31 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = -0.31 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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