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Simplifying 0 = -3x2 + -28x + -18 Reorder the terms: 0 = -18 + -28x + -3x2 Solving 0 = -18 + -28x + -3x2 Solving for variable 'x'. Combine like terms: 0 + 18 = 18 18 + 28x + 3x2 = -18 + -28x + -3x2 + 18 + 28x + 3x2 Reorder the terms: 18 + 28x + 3x2 = -18 + 18 + -28x + 28x + -3x2 + 3x2 Combine like terms: -18 + 18 = 0 18 + 28x + 3x2 = 0 + -28x + 28x + -3x2 + 3x2 18 + 28x + 3x2 = -28x + 28x + -3x2 + 3x2 Combine like terms: -28x + 28x = 0 18 + 28x + 3x2 = 0 + -3x2 + 3x2 18 + 28x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 18 + 28x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6 + 9.333333333x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 9.333333333x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 9.333333333x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 9.333333333x + x2 = 0 + -6 9.333333333x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 9.333333333x + x2 = -6 The x term is 9.333333333x. Take half its coefficient (4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. 9.333333333x + 21.77777778 + x2 = -6 + 21.77777778 Reorder the terms: 21.77777778 + 9.333333333x + x2 = -6 + 21.77777778 Combine like terms: -6 + 21.77777778 = 15.77777778 21.77777778 + 9.333333333x + x2 = 15.77777778 Factor a perfect square on the left side: (x + 4.666666667)(x + 4.666666667) = 15.77777778 Calculate the square root of the right side: 3.972125096 Break this problem into two subproblems by setting (x + 4.666666667) equal to 3.972125096 and -3.972125096.Subproblem 1
x + 4.666666667 = 3.972125096 Simplifying x + 4.666666667 = 3.972125096 Reorder the terms: 4.666666667 + x = 3.972125096 Solving 4.666666667 + x = 3.972125096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.666666667' to each side of the equation. 4.666666667 + -4.666666667 + x = 3.972125096 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + x = 3.972125096 + -4.666666667 x = 3.972125096 + -4.666666667 Combine like terms: 3.972125096 + -4.666666667 = -0.694541571 x = -0.694541571 Simplifying x = -0.694541571Subproblem 2
x + 4.666666667 = -3.972125096 Simplifying x + 4.666666667 = -3.972125096 Reorder the terms: 4.666666667 + x = -3.972125096 Solving 4.666666667 + x = -3.972125096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.666666667' to each side of the equation. 4.666666667 + -4.666666667 + x = -3.972125096 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + x = -3.972125096 + -4.666666667 x = -3.972125096 + -4.666666667 Combine like terms: -3.972125096 + -4.666666667 = -8.638791763 x = -8.638791763 Simplifying x = -8.638791763Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.694541571, -8.638791763}
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