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Simplifying f(0) = 4x2 + -7x + 7 Reorder the terms for easier multiplication: 0f = 4x2 + -7x + 7 Anything times zero is zero. 0f = 4x2 + -7x + 7 Reorder the terms: 0 = 7 + -7x + 4x2 Solving 0 = 7 + -7x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + 7x + -4x2 = 7 + -7x + 4x2 + -7 + 7x + -4x2 Reorder the terms: -7 + 7x + -4x2 = 7 + -7 + -7x + 7x + 4x2 + -4x2 Combine like terms: 7 + -7 = 0 -7 + 7x + -4x2 = 0 + -7x + 7x + 4x2 + -4x2 -7 + 7x + -4x2 = -7x + 7x + 4x2 + -4x2 Combine like terms: -7x + 7x = 0 -7 + 7x + -4x2 = 0 + 4x2 + -4x2 -7 + 7x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -7 + 7x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.75 + -1.75x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -1.75x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -1.75x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -1.75x + x2 = 0 + -1.75 -1.75x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -1.75x + x2 = -1.75 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = -1.75 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = -1.75 + 0.765625 Combine like terms: -1.75 + 0.765625 = -0.984375 0.765625 + -1.75x + x2 = -0.984375 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = -0.984375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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