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Simplifying 3x2 + 15x + -33 = 0 Reorder the terms: -33 + 15x + 3x2 = 0 Solving -33 + 15x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + 5x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + 5x + x2)' equal to zero and attempt to solve: Simplifying -11 + 5x + x2 = 0 Solving -11 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 5x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 5x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 5x + x2 = 0 + 11 5x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 5x + x2 = 11 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 = 11 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 11 + 6.25 Combine like terms: 11 + 6.25 = 17.25 6.25 + 5x + x2 = 17.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + 2.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + 2.5 = 4.153311931 Simplifying x + 2.5 = 4.153311931 Reorder the terms: 2.5 + x = 4.153311931 Solving 2.5 + x = 4.153311931 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 = 4.153311931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.153311931 + -2.5 x = 4.153311931 + -2.5 Combine like terms: 4.153311931 + -2.5 = 1.653311931 x = 1.653311931 Simplifying x = 1.653311931Subproblem 2
x + 2.5 = -4.153311931 Simplifying x + 2.5 = -4.153311931 Reorder the terms: 2.5 + x = -4.153311931 Solving 2.5 + x = -4.153311931 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 = -4.153311931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.153311931 + -2.5 x = -4.153311931 + -2.5 Combine like terms: -4.153311931 + -2.5 = -6.653311931 x = -6.653311931 Simplifying x = -6.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.653311931, -6.653311931}Solution
x = {1.653311931, -6.653311931}
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