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Simplifying -1x(5x2 + 8x + -40) = 0 Reorder the terms: -1x(-40 + 8x + 5x2) = 0 (-40 * -1x + 8x * -1x + 5x2 * -1x) = 0 (40x + -8x2 + -5x3) = 0 Solving 40x + -8x2 + -5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(40 + -8x + -5x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(40 + -8x + -5x2)' equal to zero and attempt to solve: Simplifying 40 + -8x + -5x2 = 0 Solving 40 + -8x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8 + 1.6x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 1.6x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 1.6x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 1.6x + x2 = 0 + 8 1.6x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 1.6x + x2 = 8 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 8 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 8 + 0.64 Combine like terms: 8 + 0.64 = 8.64 0.64 + 1.6x + x2 = 8.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 8.64 Calculate the square root of the right side: 2.939387691 Break this problem into two subproblems by setting (x + 0.8) equal to 2.939387691 and -2.939387691.Subproblem 1
x + 0.8 = 2.939387691 Simplifying x + 0.8 = 2.939387691 Reorder the terms: 0.8 + x = 2.939387691 Solving 0.8 + x = 2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 2.939387691 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 2.939387691 + -0.8 x = 2.939387691 + -0.8 Combine like terms: 2.939387691 + -0.8 = 2.139387691 x = 2.139387691 Simplifying x = 2.139387691Subproblem 2
x + 0.8 = -2.939387691 Simplifying x + 0.8 = -2.939387691 Reorder the terms: 0.8 + x = -2.939387691 Solving 0.8 + x = -2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -2.939387691 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -2.939387691 + -0.8 x = -2.939387691 + -0.8 Combine like terms: -2.939387691 + -0.8 = -3.739387691 x = -3.739387691 Simplifying x = -3.739387691Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.139387691, -3.739387691}Solution
x = {0, 2.139387691, -3.739387691}
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