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Simplifying -8 = -0.3x2 + x + 4 Reorder the terms: -8 = 4 + x + -0.3x2 Solving -8 = 4 + x + -0.3x2 Solving for variable 'x'. Combine like terms: -8 + -4 = -12 -12 + -1x + 0.3x2 = 4 + x + -0.3x2 + -4 + -1x + 0.3x2 Reorder the terms: -12 + -1x + 0.3x2 = 4 + -4 + x + -1x + -0.3x2 + 0.3x2 Combine like terms: 4 + -4 = 0 -12 + -1x + 0.3x2 = 0 + x + -1x + -0.3x2 + 0.3x2 -12 + -1x + 0.3x2 = x + -1x + -0.3x2 + 0.3x2 Combine like terms: x + -1x = 0 -12 + -1x + 0.3x2 = 0 + -0.3x2 + 0.3x2 -12 + -1x + 0.3x2 = -0.3x2 + 0.3x2 Combine like terms: -0.3x2 + 0.3x2 = 0.0 -12 + -1x + 0.3x2 = 0.0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -40 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -3.333333333x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -3.333333333x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -3.333333333x + x2 = 0 + 40 -3.333333333x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -3.333333333x + x2 = 40 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 40 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 40 + 2.777777779 Combine like terms: 40 + 2.777777779 = 42.777777779 2.777777779 + -3.333333333x + x2 = 42.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 42.777777779 Calculate the square root of the right side: 6.54047229 Break this problem into two subproblems by setting (x + -1.666666667) equal to 6.54047229 and -6.54047229.Subproblem 1
x + -1.666666667 = 6.54047229 Simplifying x + -1.666666667 = 6.54047229 Reorder the terms: -1.666666667 + x = 6.54047229 Solving -1.666666667 + x = 6.54047229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 6.54047229 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 6.54047229 + 1.666666667 x = 6.54047229 + 1.666666667 Combine like terms: 6.54047229 + 1.666666667 = 8.207138957 x = 8.207138957 Simplifying x = 8.207138957Subproblem 2
x + -1.666666667 = -6.54047229 Simplifying x + -1.666666667 = -6.54047229 Reorder the terms: -1.666666667 + x = -6.54047229 Solving -1.666666667 + x = -6.54047229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -6.54047229 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -6.54047229 + 1.666666667 x = -6.54047229 + 1.666666667 Combine like terms: -6.54047229 + 1.666666667 = -4.873805623 x = -4.873805623 Simplifying x = -4.873805623Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.207138957, -4.873805623}
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