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Simplifying 0 = 16x2 + 7x + 10 Reorder the terms: 0 = 10 + 7x + 16x2 Solving 0 = 10 + 7x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -7x + -16x2 = 10 + 7x + 16x2 + -10 + -7x + -16x2 Reorder the terms: -10 + -7x + -16x2 = 10 + -10 + 7x + -7x + 16x2 + -16x2 Combine like terms: 10 + -10 = 0 -10 + -7x + -16x2 = 0 + 7x + -7x + 16x2 + -16x2 -10 + -7x + -16x2 = 7x + -7x + 16x2 + -16x2 Combine like terms: 7x + -7x = 0 -10 + -7x + -16x2 = 0 + 16x2 + -16x2 -10 + -7x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -10 + -7x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 7x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 7x + 16x2)' equal to zero and attempt to solve: Simplifying 10 + 7x + 16x2 = 0 Solving 10 + 7x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.625 + 0.4375x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 0.4375x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 0.4375x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 0.4375x + x2 = 0 + -0.625 0.4375x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 0.4375x + x2 = -0.625 The x term is 0.4375x. Take half its coefficient (0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. 0.4375x + 0.0478515625 + x2 = -0.625 + 0.0478515625 Reorder the terms: 0.0478515625 + 0.4375x + x2 = -0.625 + 0.0478515625 Combine like terms: -0.625 + 0.0478515625 = -0.5771484375 0.0478515625 + 0.4375x + x2 = -0.5771484375 Factor a perfect square on the left side: (x + 0.21875)(x + 0.21875) = -0.5771484375 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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