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Simplifying 0 = 5x2 + -24x + 37 Reorder the terms: 0 = 37 + -24x + 5x2 Solving 0 = 37 + -24x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -37 = -37 -37 + 24x + -5x2 = 37 + -24x + 5x2 + -37 + 24x + -5x2 Reorder the terms: -37 + 24x + -5x2 = 37 + -37 + -24x + 24x + 5x2 + -5x2 Combine like terms: 37 + -37 = 0 -37 + 24x + -5x2 = 0 + -24x + 24x + 5x2 + -5x2 -37 + 24x + -5x2 = -24x + 24x + 5x2 + -5x2 Combine like terms: -24x + 24x = 0 -37 + 24x + -5x2 = 0 + 5x2 + -5x2 -37 + 24x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -37 + 24x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 7.4 + -4.8x + x2 = 0 Move the constant term to the right: Add '-7.4' to each side of the equation. 7.4 + -4.8x + -7.4 + x2 = 0 + -7.4 Reorder the terms: 7.4 + -7.4 + -4.8x + x2 = 0 + -7.4 Combine like terms: 7.4 + -7.4 = 0.0 0.0 + -4.8x + x2 = 0 + -7.4 -4.8x + x2 = 0 + -7.4 Combine like terms: 0 + -7.4 = -7.4 -4.8x + x2 = -7.4 The x term is -4.8x. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x + 5.76 + x2 = -7.4 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = -7.4 + 5.76 Combine like terms: -7.4 + 5.76 = -1.64 5.76 + -4.8x + x2 = -1.64 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = -1.64 Can't calculate square root of the right side. The solution to this equation could not be determined.
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