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Simplifying 2x2 + -6x = 50 Reorder the terms: -6x + 2x2 = 50 Solving -6x + 2x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + -6x + 2x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -3x + x2)' equal to zero and attempt to solve: Simplifying -25 + -3x + x2 = 0 Solving -25 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -3x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -3x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -3x + x2 = 0 + 25 -3x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -3x + x2 = 25 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 25 + 2.25 Combine like terms: 25 + 2.25 = 27.25 2.25 + -3x + x2 = 27.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + -1.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + -1.5 = 5.220153254 Simplifying x + -1.5 = 5.220153254 Reorder the terms: -1.5 + x = 5.220153254 Solving -1.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.220153254 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.220153254 + 1.5 x = 5.220153254 + 1.5 Combine like terms: 5.220153254 + 1.5 = 6.720153254 x = 6.720153254 Simplifying x = 6.720153254Subproblem 2
x + -1.5 = -5.220153254 Simplifying x + -1.5 = -5.220153254 Reorder the terms: -1.5 + x = -5.220153254 Solving -1.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.220153254 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.220153254 + 1.5 x = -5.220153254 + 1.5 Combine like terms: -5.220153254 + 1.5 = -3.720153254 x = -3.720153254 Simplifying x = -3.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.720153254, -3.720153254}Solution
x = {6.720153254, -3.720153254}
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