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Simplifying (8x2 + -6x + 10) + -1(3x2 + -7x + -4) = 0 Reorder the terms: (10 + -6x + 8x2) + -1(3x2 + -7x + -4) = 0 Remove parenthesis around (10 + -6x + 8x2) 10 + -6x + 8x2 + -1(3x2 + -7x + -4) = 0 Reorder the terms: 10 + -6x + 8x2 + -1(-4 + -7x + 3x2) = 0 10 + -6x + 8x2 + (-4 * -1 + -7x * -1 + 3x2 * -1) = 0 10 + -6x + 8x2 + (4 + 7x + -3x2) = 0 Reorder the terms: 10 + 4 + -6x + 7x + 8x2 + -3x2 = 0 Combine like terms: 10 + 4 = 14 14 + -6x + 7x + 8x2 + -3x2 = 0 Combine like terms: -6x + 7x = 1x 14 + 1x + 8x2 + -3x2 = 0 Combine like terms: 8x2 + -3x2 = 5x2 14 + 1x + 5x2 = 0 Solving 14 + 1x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + 0.2x + x2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + 0.2x + -2.8 + x2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + 0.2x + x2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 0.2x + x2 = 0 + -2.8 0.2x + x2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 0.2x + x2 = -2.8 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = -2.8 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = -2.8 + 0.01 Combine like terms: -2.8 + 0.01 = -2.79 0.01 + 0.2x + x2 = -2.79 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = -2.79 Can't calculate square root of the right side. The solution to this equation could not be determined.
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