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Simplifying (5x2 + 3x + -4) + -1(3x2 + -5x + 4) = 0 Reorder the terms: (-4 + 3x + 5x2) + -1(3x2 + -5x + 4) = 0 Remove parenthesis around (-4 + 3x + 5x2) -4 + 3x + 5x2 + -1(3x2 + -5x + 4) = 0 Reorder the terms: -4 + 3x + 5x2 + -1(4 + -5x + 3x2) = 0 -4 + 3x + 5x2 + (4 * -1 + -5x * -1 + 3x2 * -1) = 0 -4 + 3x + 5x2 + (-4 + 5x + -3x2) = 0 Reorder the terms: -4 + -4 + 3x + 5x + 5x2 + -3x2 = 0 Combine like terms: -4 + -4 = -8 -8 + 3x + 5x + 5x2 + -3x2 = 0 Combine like terms: 3x + 5x = 8x -8 + 8x + 5x2 + -3x2 = 0 Combine like terms: 5x2 + -3x2 = 2x2 -8 + 8x + 2x2 = 0 Solving -8 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 4x + x2)' equal to zero and attempt to solve: Simplifying -4 + 4x + x2 = 0 Solving -4 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4x + x2 = 0 + 4 4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 4x + x2 = 4 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 4 + 4 Reorder the terms: 4 + 4x + x2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + 4x + x2 = 8 Factor a perfect square on the left side: (x + 2)(x + 2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 2) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 2 = 2.828427125 Simplifying x + 2 = 2.828427125 Reorder the terms: 2 + x = 2.828427125 Solving 2 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.828427125 + -2 x = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 x = 0.828427125 Simplifying x = 0.828427125Subproblem 2
x + 2 = -2.828427125 Simplifying x + 2 = -2.828427125 Reorder the terms: 2 + x = -2.828427125 Solving 2 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.828427125 + -2 x = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 x = -4.828427125 Simplifying x = -4.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.828427125, -4.828427125}Solution
x = {0.828427125, -4.828427125}
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