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Simplifying 5x(-4 + -3x) + -1(2x + x3) = 0 (-4 * 5x + -3x * 5x) + -1(2x + x3) = 0 (-20x + -15x2) + -1(2x + x3) = 0 -20x + -15x2 + (2x * -1 + x3 * -1) = 0 -20x + -15x2 + (-2x + -1x3) = 0 Reorder the terms: -20x + -2x + -15x2 + -1x3 = 0 Combine like terms: -20x + -2x = -22x -22x + -15x2 + -1x3 = 0 Solving -22x + -15x2 + -1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1x'. -1x(22 + 15x + x2) = 0 Ignore the factor -1.Subproblem 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 '(22 + 15x + x2)' equal to zero and attempt to solve: Simplifying 22 + 15x + x2 = 0 Solving 22 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 15x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + 15x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 15x + x2 = 0 + -22 15x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 15x + x2 = -22 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -22 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -22 + 56.25 Combine like terms: -22 + 56.25 = 34.25 56.25 + 15x + x2 = 34.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + 7.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + 7.5 = 5.852349955 Simplifying x + 7.5 = 5.852349955 Reorder the terms: 7.5 + x = 5.852349955 Solving 7.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 5.852349955 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 5.852349955 + -7.5 x = 5.852349955 + -7.5 Combine like terms: 5.852349955 + -7.5 = -1.647650045 x = -1.647650045 Simplifying x = -1.647650045Subproblem 2
x + 7.5 = -5.852349955 Simplifying x + 7.5 = -5.852349955 Reorder the terms: 7.5 + x = -5.852349955 Solving 7.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -5.852349955 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -5.852349955 + -7.5 x = -5.852349955 + -7.5 Combine like terms: -5.852349955 + -7.5 = -13.352349955 x = -13.352349955 Simplifying x = -13.352349955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.647650045, -13.352349955}Solution
x = {0, -1.647650045, -13.352349955}
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