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Simplifying 2x2 + -7x + 28 = -10x2 + 13x + 15 Reorder the terms: 28 + -7x + 2x2 = -10x2 + 13x + 15 Reorder the terms: 28 + -7x + 2x2 = 15 + 13x + -10x2 Solving 28 + -7x + 2x2 = 15 + 13x + -10x2 Solving for variable 'x'. Reorder the terms: 28 + -15 + -7x + -13x + 2x2 + 10x2 = 15 + 13x + -10x2 + -15 + -13x + 10x2 Combine like terms: 28 + -15 = 13 13 + -7x + -13x + 2x2 + 10x2 = 15 + 13x + -10x2 + -15 + -13x + 10x2 Combine like terms: -7x + -13x = -20x 13 + -20x + 2x2 + 10x2 = 15 + 13x + -10x2 + -15 + -13x + 10x2 Combine like terms: 2x2 + 10x2 = 12x2 13 + -20x + 12x2 = 15 + 13x + -10x2 + -15 + -13x + 10x2 Reorder the terms: 13 + -20x + 12x2 = 15 + -15 + 13x + -13x + -10x2 + 10x2 Combine like terms: 15 + -15 = 0 13 + -20x + 12x2 = 0 + 13x + -13x + -10x2 + 10x2 13 + -20x + 12x2 = 13x + -13x + -10x2 + 10x2 Combine like terms: 13x + -13x = 0 13 + -20x + 12x2 = 0 + -10x2 + 10x2 13 + -20x + 12x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 13 + -20x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.083333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-1.083333333' to each side of the equation. 1.083333333 + -1.666666667x + -1.083333333 + x2 = 0 + -1.083333333 Reorder the terms: 1.083333333 + -1.083333333 + -1.666666667x + x2 = 0 + -1.083333333 Combine like terms: 1.083333333 + -1.083333333 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + -1.083333333 -1.666666667x + x2 = 0 + -1.083333333 Combine like terms: 0 + -1.083333333 = -1.083333333 -1.666666667x + x2 = -1.083333333 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = -1.083333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -1.083333333 + 0.6944444447 Combine like terms: -1.083333333 + 0.6944444447 = -0.3888888883 0.6944444447 + -1.666666667x + x2 = -0.3888888883 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = -0.3888888883 Can't calculate square root of the right side. The solution to this equation could not be determined.
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