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Simplifying 3x2 + -27x = -3x2 + -2x + -18 Reorder the terms: -27x + 3x2 = -3x2 + -2x + -18 Reorder the terms: -27x + 3x2 = -18 + -2x + -3x2 Solving -27x + 3x2 = -18 + -2x + -3x2 Solving for variable 'x'. Reorder the terms: 18 + -27x + 2x + 3x2 + 3x2 = -18 + -2x + -3x2 + 18 + 2x + 3x2 Combine like terms: -27x + 2x = -25x 18 + -25x + 3x2 + 3x2 = -18 + -2x + -3x2 + 18 + 2x + 3x2 Combine like terms: 3x2 + 3x2 = 6x2 18 + -25x + 6x2 = -18 + -2x + -3x2 + 18 + 2x + 3x2 Reorder the terms: 18 + -25x + 6x2 = -18 + 18 + -2x + 2x + -3x2 + 3x2 Combine like terms: -18 + 18 = 0 18 + -25x + 6x2 = 0 + -2x + 2x + -3x2 + 3x2 18 + -25x + 6x2 = -2x + 2x + -3x2 + 3x2 Combine like terms: -2x + 2x = 0 18 + -25x + 6x2 = 0 + -3x2 + 3x2 18 + -25x + 6x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 18 + -25x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3 + -4.166666667x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.166666667x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4.166666667x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.166666667x + x2 = 0 + -3 -4.166666667x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.166666667x + x2 = -3 The x term is -4.166666667x. Take half its coefficient (-2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. -4.166666667x + 4.340277781 + x2 = -3 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667x + x2 = -3 + 4.340277781 Combine like terms: -3 + 4.340277781 = 1.340277781 4.340277781 + -4.166666667x + x2 = 1.340277781 Factor a perfect square on the left side: (x + -2.083333334)(x + -2.083333334) = 1.340277781 Calculate the square root of the right side: 1.157703667 Break this problem into two subproblems by setting (x + -2.083333334) equal to 1.157703667 and -1.157703667.Subproblem 1
x + -2.083333334 = 1.157703667 Simplifying x + -2.083333334 = 1.157703667 Reorder the terms: -2.083333334 + x = 1.157703667 Solving -2.083333334 + x = 1.157703667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = 1.157703667 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = 1.157703667 + 2.083333334 x = 1.157703667 + 2.083333334 Combine like terms: 1.157703667 + 2.083333334 = 3.241037001 x = 3.241037001 Simplifying x = 3.241037001Subproblem 2
x + -2.083333334 = -1.157703667 Simplifying x + -2.083333334 = -1.157703667 Reorder the terms: -2.083333334 + x = -1.157703667 Solving -2.083333334 + x = -1.157703667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = -1.157703667 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = -1.157703667 + 2.083333334 x = -1.157703667 + 2.083333334 Combine like terms: -1.157703667 + 2.083333334 = 0.925629667 x = 0.925629667 Simplifying x = 0.925629667Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.241037001, 0.925629667}
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