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Simplifying 61.5 = -0.5(x + -175)(x + -175) Reorder the terms: 61.5 = -0.5(-175 + x)(x + -175) Reorder the terms: 61.5 = -0.5(-175 + x)(-175 + x) Multiply (-175 + x) * (-175 + x) 61.5 = -0.5(-175(-175 + x) + x(-175 + x)) 61.5 = -0.5((-175 * -175 + x * -175) + x(-175 + x)) 61.5 = -0.5((30625 + -175x) + x(-175 + x)) 61.5 = -0.5(30625 + -175x + (-175 * x + x * x)) 61.5 = -0.5(30625 + -175x + (-175x + x2)) Combine like terms: -175x + -175x = -350x 61.5 = -0.5(30625 + -350x + x2) 61.5 = (30625 * -0.5 + -350x * -0.5 + x2 * -0.5) 61.5 = (-15312.5 + 175x + -0.5x2) Solving 61.5 = -15312.5 + 175x + -0.5x2 Solving for variable 'x'. Combine like terms: 61.5 + 15312.5 = 15374 15374 + -175x + 0.5x2 = -15312.5 + 175x + -0.5x2 + 15312.5 + -175x + 0.5x2 Reorder the terms: 15374 + -175x + 0.5x2 = -15312.5 + 15312.5 + 175x + -175x + -0.5x2 + 0.5x2 Combine like terms: -15312.5 + 15312.5 = 0.0 15374 + -175x + 0.5x2 = 0.0 + 175x + -175x + -0.5x2 + 0.5x2 15374 + -175x + 0.5x2 = 175x + -175x + -0.5x2 + 0.5x2 Combine like terms: 175x + -175x = 0 15374 + -175x + 0.5x2 = 0 + -0.5x2 + 0.5x2 15374 + -175x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 15374 + -175x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 30748 + -350x + x2 = 0 Move the constant term to the right: Add '-30748' to each side of the equation. 30748 + -350x + -30748 + x2 = 0 + -30748 Reorder the terms: 30748 + -30748 + -350x + x2 = 0 + -30748 Combine like terms: 30748 + -30748 = 0 0 + -350x + x2 = 0 + -30748 -350x + x2 = 0 + -30748 Combine like terms: 0 + -30748 = -30748 -350x + x2 = -30748 The x term is -350x. Take half its coefficient (-175). Square it (30625) and add it to both sides. Add '30625' to each side of the equation. -350x + 30625 + x2 = -30748 + 30625 Reorder the terms: 30625 + -350x + x2 = -30748 + 30625 Combine like terms: -30748 + 30625 = -123 30625 + -350x + x2 = -123 Factor a perfect square on the left side: (x + -175)(x + -175) = -123 Can't calculate square root of the right side. The solution to this equation could not be determined.
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