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Simplifying 0.4x(6x + 12) = 1.1 + -1(x + 2) Reorder the terms: 0.4x(12 + 6x) = 1.1 + -1(x + 2) (12 * 0.4x + 6x * 0.4x) = 1.1 + -1(x + 2) (4.8x + 2.4x2) = 1.1 + -1(x + 2) Reorder the terms: 4.8x + 2.4x2 = 1.1 + -1(2 + x) 4.8x + 2.4x2 = 1.1 + (2 * -1 + x * -1) 4.8x + 2.4x2 = 1.1 + (-2 + -1x) Combine like terms: 1.1 + -2 = -0.9 4.8x + 2.4x2 = -0.9 + -1x Solving 4.8x + 2.4x2 = -0.9 + -1x Solving for variable 'x'. Reorder the terms: 0.9 + 4.8x + x + 2.4x2 = -0.9 + -1x + 0.9 + x Combine like terms: 4.8x + x = 5.8x 0.9 + 5.8x + 2.4x2 = -0.9 + -1x + 0.9 + x Reorder the terms: 0.9 + 5.8x + 2.4x2 = -0.9 + 0.9 + -1x + x Combine like terms: -0.9 + 0.9 = 0.0 0.9 + 5.8x + 2.4x2 = 0.0 + -1x + x 0.9 + 5.8x + 2.4x2 = -1x + x Combine like terms: -1x + x = 0 0.9 + 5.8x + 2.4x2 = 0 Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. 0.375 + 2.416666667x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 2.416666667x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 2.416666667x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 2.416666667x + x2 = 0 + -0.375 2.416666667x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 2.416666667x + x2 = -0.375 The x term is 2.416666667x. Take half its coefficient (1.208333334). Square it (1.460069446) and add it to both sides. Add '1.460069446' to each side of the equation. 2.416666667x + 1.460069446 + x2 = -0.375 + 1.460069446 Reorder the terms: 1.460069446 + 2.416666667x + x2 = -0.375 + 1.460069446 Combine like terms: -0.375 + 1.460069446 = 1.085069446 1.460069446 + 2.416666667x + x2 = 1.085069446 Factor a perfect square on the left side: (x + 1.208333334)(x + 1.208333334) = 1.085069446 Calculate the square root of the right side: 1.041666667 Break this problem into two subproblems by setting (x + 1.208333334) equal to 1.041666667 and -1.041666667.Subproblem 1
x + 1.208333334 = 1.041666667 Simplifying x + 1.208333334 = 1.041666667 Reorder the terms: 1.208333334 + x = 1.041666667 Solving 1.208333334 + x = 1.041666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + x = 1.041666667 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + x = 1.041666667 + -1.208333334 x = 1.041666667 + -1.208333334 Combine like terms: 1.041666667 + -1.208333334 = -0.166666667 x = -0.166666667 Simplifying x = -0.166666667Subproblem 2
x + 1.208333334 = -1.041666667 Simplifying x + 1.208333334 = -1.041666667 Reorder the terms: 1.208333334 + x = -1.041666667 Solving 1.208333334 + x = -1.041666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + x = -1.041666667 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + x = -1.041666667 + -1.208333334 x = -1.041666667 + -1.208333334 Combine like terms: -1.041666667 + -1.208333334 = -2.250000001 x = -2.250000001 Simplifying x = -2.250000001Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.166666667, -2.250000001}
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