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Simplifying 0 = 4x2 + 8x + 7 Reorder the terms: 0 = 7 + 8x + 4x2 Solving 0 = 7 + 8x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -8x + -4x2 = 7 + 8x + 4x2 + -7 + -8x + -4x2 Reorder the terms: -7 + -8x + -4x2 = 7 + -7 + 8x + -8x + 4x2 + -4x2 Combine like terms: 7 + -7 = 0 -7 + -8x + -4x2 = 0 + 8x + -8x + 4x2 + -4x2 -7 + -8x + -4x2 = 8x + -8x + 4x2 + -4x2 Combine like terms: 8x + -8x = 0 -7 + -8x + -4x2 = 0 + 4x2 + -4x2 -7 + -8x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -7 + -8x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 8x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 8x + 4x2)' equal to zero and attempt to solve: Simplifying 7 + 8x + 4x2 = 0 Solving 7 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 2x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 2x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 2x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 2x + x2 = 0 + -1.75 2x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 2x + x2 = -1.75 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -1.75 + 1 Reorder the terms: 1 + 2x + x2 = -1.75 + 1 Combine like terms: -1.75 + 1 = -0.75 1 + 2x + x2 = -0.75 Factor a perfect square on the left side: (x + 1)(x + 1) = -0.75 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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