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Simplifying 50x(3x + -4) = 2(3x + -4) + 26 Reorder the terms: 50x(-4 + 3x) = 2(3x + -4) + 26 (-4 * 50x + 3x * 50x) = 2(3x + -4) + 26 (-200x + 150x2) = 2(3x + -4) + 26 Reorder the terms: -200x + 150x2 = 2(-4 + 3x) + 26 -200x + 150x2 = (-4 * 2 + 3x * 2) + 26 -200x + 150x2 = (-8 + 6x) + 26 Reorder the terms: -200x + 150x2 = -8 + 26 + 6x Combine like terms: -8 + 26 = 18 -200x + 150x2 = 18 + 6x Solving -200x + 150x2 = 18 + 6x Solving for variable 'x'. Reorder the terms: -18 + -200x + -6x + 150x2 = 18 + 6x + -18 + -6x Combine like terms: -200x + -6x = -206x -18 + -206x + 150x2 = 18 + 6x + -18 + -6x Reorder the terms: -18 + -206x + 150x2 = 18 + -18 + 6x + -6x Combine like terms: 18 + -18 = 0 -18 + -206x + 150x2 = 0 + 6x + -6x -18 + -206x + 150x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -18 + -206x + 150x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -103x + 75x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -103x + 75x2)' equal to zero and attempt to solve: Simplifying -9 + -103x + 75x2 = 0 Solving -9 + -103x + 75x2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. -0.12 + -1.373333333x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -1.373333333x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + -1.373333333x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -1.373333333x + x2 = 0 + 0.12 -1.373333333x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 -1.373333333x + x2 = 0.12 The x term is -1.373333333x. Take half its coefficient (-0.6866666665). Square it (0.4715111109) and add it to both sides. Add '0.4715111109' to each side of the equation. -1.373333333x + 0.4715111109 + x2 = 0.12 + 0.4715111109 Reorder the terms: 0.4715111109 + -1.373333333x + x2 = 0.12 + 0.4715111109 Combine like terms: 0.12 + 0.4715111109 = 0.5915111109 0.4715111109 + -1.373333333x + x2 = 0.5915111109 Factor a perfect square on the left side: (x + -0.6866666665)(x + -0.6866666665) = 0.5915111109 Calculate the square root of the right side: 0.769097595 Break this problem into two subproblems by setting (x + -0.6866666665) equal to 0.769097595 and -0.769097595.Subproblem 1
x + -0.6866666665 = 0.769097595 Simplifying x + -0.6866666665 = 0.769097595 Reorder the terms: -0.6866666665 + x = 0.769097595 Solving -0.6866666665 + x = 0.769097595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6866666665' to each side of the equation. -0.6866666665 + 0.6866666665 + x = 0.769097595 + 0.6866666665 Combine like terms: -0.6866666665 + 0.6866666665 = 0.0000000000 0.0000000000 + x = 0.769097595 + 0.6866666665 x = 0.769097595 + 0.6866666665 Combine like terms: 0.769097595 + 0.6866666665 = 1.4557642615 x = 1.4557642615 Simplifying x = 1.4557642615Subproblem 2
x + -0.6866666665 = -0.769097595 Simplifying x + -0.6866666665 = -0.769097595 Reorder the terms: -0.6866666665 + x = -0.769097595 Solving -0.6866666665 + x = -0.769097595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6866666665' to each side of the equation. -0.6866666665 + 0.6866666665 + x = -0.769097595 + 0.6866666665 Combine like terms: -0.6866666665 + 0.6866666665 = 0.0000000000 0.0000000000 + x = -0.769097595 + 0.6866666665 x = -0.769097595 + 0.6866666665 Combine like terms: -0.769097595 + 0.6866666665 = -0.0824309285 x = -0.0824309285 Simplifying x = -0.0824309285Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4557642615, -0.0824309285}Solution
x = {1.4557642615, -0.0824309285}
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