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Simplifying 2x2 + -18x = 5x2 + -3x + -8 Reorder the terms: -18x + 2x2 = 5x2 + -3x + -8 Reorder the terms: -18x + 2x2 = -8 + -3x + 5x2 Solving -18x + 2x2 = -8 + -3x + 5x2 Solving for variable 'x'. Reorder the terms: 8 + -18x + 3x + 2x2 + -5x2 = -8 + -3x + 5x2 + 8 + 3x + -5x2 Combine like terms: -18x + 3x = -15x 8 + -15x + 2x2 + -5x2 = -8 + -3x + 5x2 + 8 + 3x + -5x2 Combine like terms: 2x2 + -5x2 = -3x2 8 + -15x + -3x2 = -8 + -3x + 5x2 + 8 + 3x + -5x2 Reorder the terms: 8 + -15x + -3x2 = -8 + 8 + -3x + 3x + 5x2 + -5x2 Combine like terms: -8 + 8 = 0 8 + -15x + -3x2 = 0 + -3x + 3x + 5x2 + -5x2 8 + -15x + -3x2 = -3x + 3x + 5x2 + -5x2 Combine like terms: -3x + 3x = 0 8 + -15x + -3x2 = 0 + 5x2 + -5x2 8 + -15x + -3x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 8 + -15x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.666666667 + 5x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 5x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 5x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 5x + x2 = 0 + 2.666666667 5x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 5x + x2 = 2.666666667 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 2.666666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 2.666666667 + 6.25 Combine like terms: 2.666666667 + 6.25 = 8.916666667 6.25 + 5x + x2 = 8.916666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 8.916666667 Calculate the square root of the right side: 2.986078811 Break this problem into two subproblems by setting (x + 2.5) equal to 2.986078811 and -2.986078811.Subproblem 1
x + 2.5 = 2.986078811 Simplifying x + 2.5 = 2.986078811 Reorder the terms: 2.5 + x = 2.986078811 Solving 2.5 + x = 2.986078811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.986078811 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.986078811 + -2.5 x = 2.986078811 + -2.5 Combine like terms: 2.986078811 + -2.5 = 0.486078811 x = 0.486078811 Simplifying x = 0.486078811Subproblem 2
x + 2.5 = -2.986078811 Simplifying x + 2.5 = -2.986078811 Reorder the terms: 2.5 + x = -2.986078811 Solving 2.5 + x = -2.986078811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.986078811 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.986078811 + -2.5 x = -2.986078811 + -2.5 Combine like terms: -2.986078811 + -2.5 = -5.486078811 x = -5.486078811 Simplifying x = -5.486078811Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.486078811, -5.486078811}
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