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Simplifying 0.107 = 0.14x(1 + -1x) * 0.085 * 0.65 Reorder the terms for easier multiplication: 0.107 = 0.14 * 0.085 * 0.65x(1 + -1x) Multiply 0.14 * 0.085 0.107 = 0.0119 * 0.65x(1 + -1x) Multiply 0.0119 * 0.65 0.107 = 0.007735x(1 + -1x) 0.107 = (1 * 0.007735x + -1x * 0.007735x) 0.107 = (0.007735x + -0.007735x2) Solving 0.107 = 0.007735x + -0.007735x2 Solving for variable 'x'. Reorder the terms: 0.107 + -0.007735x + 0.007735x2 = 0.007735x + -0.007735x + -0.007735x2 + 0.007735x2 Combine like terms: 0.007735x + -0.007735x = 0.000000 0.107 + -0.007735x + 0.007735x2 = 0.000000 + -0.007735x2 + 0.007735x2 0.107 + -0.007735x + 0.007735x2 = -0.007735x2 + 0.007735x2 Combine like terms: -0.007735x2 + 0.007735x2 = 0.000000 0.107 + -0.007735x + 0.007735x2 = 0.000000 Begin completing the square. Divide all terms by 0.007735 the coefficient of the squared term: Divide each side by '0.007735'. 13.8332256 + -1x + x2 = 0 Move the constant term to the right: Add '-13.8332256' to each side of the equation. 13.8332256 + -1x + -13.8332256 + x2 = 0 + -13.8332256 Reorder the terms: 13.8332256 + -13.8332256 + -1x + x2 = 0 + -13.8332256 Combine like terms: 13.8332256 + -13.8332256 = 0.0000000 0.0000000 + -1x + x2 = 0 + -13.8332256 -1x + x2 = 0 + -13.8332256 Combine like terms: 0 + -13.8332256 = -13.8332256 -1x + x2 = -13.8332256 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -13.8332256 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -13.8332256 + 0.25 Combine like terms: -13.8332256 + 0.25 = -13.5832256 0.25 + -1x + x2 = -13.5832256 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -13.5832256 Can't calculate square root of the right side. The solution to this equation could not be determined.
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