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Simplifying x(4x + -3) + 5 = 4(x + -4x) + -19 Reorder the terms: x(-3 + 4x) + 5 = 4(x + -4x) + -19 (-3 * x + 4x * x) + 5 = 4(x + -4x) + -19 (-3x + 4x2) + 5 = 4(x + -4x) + -19 Reorder the terms: 5 + -3x + 4x2 = 4(x + -4x) + -19 Combine like terms: x + -4x = -3x 5 + -3x + 4x2 = 4(-3x) + -19 Remove parenthesis around (-3x) 5 + -3x + 4x2 = 4 * -3x + -19 Multiply 4 * -3 5 + -3x + 4x2 = -12x + -19 Reorder the terms: 5 + -3x + 4x2 = -19 + -12x Solving 5 + -3x + 4x2 = -19 + -12x Solving for variable 'x'. Reorder the terms: 5 + 19 + -3x + 12x + 4x2 = -19 + -12x + 19 + 12x Combine like terms: 5 + 19 = 24 24 + -3x + 12x + 4x2 = -19 + -12x + 19 + 12x Combine like terms: -3x + 12x = 9x 24 + 9x + 4x2 = -19 + -12x + 19 + 12x Reorder the terms: 24 + 9x + 4x2 = -19 + 19 + -12x + 12x Combine like terms: -19 + 19 = 0 24 + 9x + 4x2 = 0 + -12x + 12x 24 + 9x + 4x2 = -12x + 12x Combine like terms: -12x + 12x = 0 24 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6 + 2.25x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 2.25x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 2.25x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 2.25x + x2 = 0 + -6 2.25x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 2.25x + x2 = -6 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = -6 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = -6 + 1.265625 Combine like terms: -6 + 1.265625 = -4.734375 1.265625 + 2.25x + x2 = -4.734375 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = -4.734375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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