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Simplifying 2.5x + 15 + 0.5x(x + -4) = 1.2x + 2(0.9x + -6) Reorder the terms: 2.5x + 15 + 0.5x(-4 + x) = 1.2x + 2(0.9x + -6) 2.5x + 15 + (-4 * 0.5x + x * 0.5x) = 1.2x + 2(0.9x + -6) 2.5x + 15 + (-2x + 0.5x2) = 1.2x + 2(0.9x + -6) Reorder the terms: 15 + 2.5x + -2x + 0.5x2 = 1.2x + 2(0.9x + -6) Combine like terms: 2.5x + -2x = 0.5x 15 + 0.5x + 0.5x2 = 1.2x + 2(0.9x + -6) Reorder the terms: 15 + 0.5x + 0.5x2 = 1.2x + 2(-6 + 0.9x) 15 + 0.5x + 0.5x2 = 1.2x + (-6 * 2 + 0.9x * 2) 15 + 0.5x + 0.5x2 = 1.2x + (-12 + 1.8x) Reorder the terms: 15 + 0.5x + 0.5x2 = -12 + 1.2x + 1.8x Combine like terms: 1.2x + 1.8x = 3x 15 + 0.5x + 0.5x2 = -12 + 3x Solving 15 + 0.5x + 0.5x2 = -12 + 3x Solving for variable 'x'. Reorder the terms: 15 + 12 + 0.5x + -3x + 0.5x2 = -12 + 3x + 12 + -3x Combine like terms: 15 + 12 = 27 27 + 0.5x + -3x + 0.5x2 = -12 + 3x + 12 + -3x Combine like terms: 0.5x + -3x = -2.5x 27 + -2.5x + 0.5x2 = -12 + 3x + 12 + -3x Reorder the terms: 27 + -2.5x + 0.5x2 = -12 + 12 + 3x + -3x Combine like terms: -12 + 12 = 0 27 + -2.5x + 0.5x2 = 0 + 3x + -3x 27 + -2.5x + 0.5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 27 + -2.5x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 54 + -5x + x2 = 0 Move the constant term to the right: Add '-54' to each side of the equation. 54 + -5x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -5x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -5x + x2 = 0 + -54 -5x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -5x + x2 = -54 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -54 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -54 + 6.25 Combine like terms: -54 + 6.25 = -47.75 6.25 + -5x + x2 = -47.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -47.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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