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Simplifying 0.4x + -0.9(9 + -3x) = -0.3x(x + -7) 0.4x + (9 * -0.9 + -3x * -0.9) = -0.3x(x + -7) 0.4x + (-8.1 + 2.7x) = -0.3x(x + -7) Reorder the terms: -8.1 + 0.4x + 2.7x = -0.3x(x + -7) Combine like terms: 0.4x + 2.7x = 3.1x -8.1 + 3.1x = -0.3x(x + -7) Reorder the terms: -8.1 + 3.1x = -0.3x(-7 + x) -8.1 + 3.1x = (-7 * -0.3x + x * -0.3x) -8.1 + 3.1x = (2.1x + -0.3x2) Solving -8.1 + 3.1x = 2.1x + -0.3x2 Solving for variable 'x'. Combine like terms: 3.1x + -2.1x = 1x -8.1 + 1x + 0.3x2 = 2.1x + -0.3x2 + -2.1x + 0.3x2 Reorder the terms: -8.1 + 1x + 0.3x2 = 2.1x + -2.1x + -0.3x2 + 0.3x2 Combine like terms: 2.1x + -2.1x = 0.0 -8.1 + 1x + 0.3x2 = 0.0 + -0.3x2 + 0.3x2 -8.1 + 1x + 0.3x2 = -0.3x2 + 0.3x2 Combine like terms: -0.3x2 + 0.3x2 = 0.0 -8.1 + 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'. -27 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + 3.333333333x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 3.333333333x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 3.333333333x + x2 = 0 + 27 3.333333333x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 3.333333333x + x2 = 27 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 = 27 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 27 + 2.777777779 Combine like terms: 27 + 2.777777779 = 29.777777779 2.777777779 + 3.333333333x + x2 = 29.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 29.777777779 Calculate the square root of the right side: 5.456901848 Break this problem into two subproblems by setting (x + 1.666666667) equal to 5.456901848 and -5.456901848.Subproblem 1
x + 1.666666667 = 5.456901848 Simplifying x + 1.666666667 = 5.456901848 Reorder the terms: 1.666666667 + x = 5.456901848 Solving 1.666666667 + x = 5.456901848 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 = 5.456901848 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 5.456901848 + -1.666666667 x = 5.456901848 + -1.666666667 Combine like terms: 5.456901848 + -1.666666667 = 3.790235181 x = 3.790235181 Simplifying x = 3.790235181Subproblem 2
x + 1.666666667 = -5.456901848 Simplifying x + 1.666666667 = -5.456901848 Reorder the terms: 1.666666667 + x = -5.456901848 Solving 1.666666667 + x = -5.456901848 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 = -5.456901848 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -5.456901848 + -1.666666667 x = -5.456901848 + -1.666666667 Combine like terms: -5.456901848 + -1.666666667 = -7.123568515 x = -7.123568515 Simplifying x = -7.123568515Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.790235181, -7.123568515}
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