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Simplifying (8x2 + 5x + -9) + -1(3x2 + -5x + 1) = 0 Reorder the terms: (-9 + 5x + 8x2) + -1(3x2 + -5x + 1) = 0 Remove parenthesis around (-9 + 5x + 8x2) -9 + 5x + 8x2 + -1(3x2 + -5x + 1) = 0 Reorder the terms: -9 + 5x + 8x2 + -1(1 + -5x + 3x2) = 0 -9 + 5x + 8x2 + (1 * -1 + -5x * -1 + 3x2 * -1) = 0 -9 + 5x + 8x2 + (-1 + 5x + -3x2) = 0 Reorder the terms: -9 + -1 + 5x + 5x + 8x2 + -3x2 = 0 Combine like terms: -9 + -1 = -10 -10 + 5x + 5x + 8x2 + -3x2 = 0 Combine like terms: 5x + 5x = 10x -10 + 10x + 8x2 + -3x2 = 0 Combine like terms: 8x2 + -3x2 = 5x2 -10 + 10x + 5x2 = 0 Solving -10 + 10x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 2x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + 2x + x2)' equal to zero and attempt to solve: Simplifying -2 + 2x + x2 = 0 Solving -2 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 2x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2x + x2 = 0 + 2 2x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2x + x2 = 2 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 2 + 1 Reorder the terms: 1 + 2x + x2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + 2x + x2 = 3 Factor a perfect square on the left side: (x + 1)(x + 1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 1) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 1 = 1.732050808 Simplifying x + 1 = 1.732050808 Reorder the terms: 1 + x = 1.732050808 Solving 1 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.732050808 + -1 x = 1.732050808 + -1 Combine like terms: 1.732050808 + -1 = 0.732050808 x = 0.732050808 Simplifying x = 0.732050808Subproblem 2
x + 1 = -1.732050808 Simplifying x + 1 = -1.732050808 Reorder the terms: 1 + x = -1.732050808 Solving 1 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.732050808 + -1 x = -1.732050808 + -1 Combine like terms: -1.732050808 + -1 = -2.732050808 x = -2.732050808 Simplifying x = -2.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.732050808, -2.732050808}Solution
x = {0.732050808, -2.732050808}
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