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Simplifying -3x2 + -9x + 20 = 0 Reorder the terms: 20 + -9x + -3x2 = 0 Solving 20 + -9x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -6.666666667 + 3x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + 3x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + 3x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + 3x + x2 = 0 + 6.666666667 3x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 3x + x2 = 6.666666667 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 6.666666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 6.666666667 + 2.25 Combine like terms: 6.666666667 + 2.25 = 8.916666667 2.25 + 3x + x2 = 8.916666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 8.916666667 Calculate the square root of the right side: 2.986078811 Break this problem into two subproblems by setting (x + 1.5) equal to 2.986078811 and -2.986078811.Subproblem 1
x + 1.5 = 2.986078811 Simplifying x + 1.5 = 2.986078811 Reorder the terms: 1.5 + x = 2.986078811 Solving 1.5 + x = 2.986078811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.986078811 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.986078811 + -1.5 x = 2.986078811 + -1.5 Combine like terms: 2.986078811 + -1.5 = 1.486078811 x = 1.486078811 Simplifying x = 1.486078811Subproblem 2
x + 1.5 = -2.986078811 Simplifying x + 1.5 = -2.986078811 Reorder the terms: 1.5 + x = -2.986078811 Solving 1.5 + x = -2.986078811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.986078811 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.986078811 + -1.5 x = -2.986078811 + -1.5 Combine like terms: -2.986078811 + -1.5 = -4.486078811 x = -4.486078811 Simplifying x = -4.486078811Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.486078811, -4.486078811}
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