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Simplifying 0 = 4x2 + 100x + -150 Reorder the terms: 0 = -150 + 100x + 4x2 Solving 0 = -150 + 100x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 150 = 150 150 + -100x + -4x2 = -150 + 100x + 4x2 + 150 + -100x + -4x2 Reorder the terms: 150 + -100x + -4x2 = -150 + 150 + 100x + -100x + 4x2 + -4x2 Combine like terms: -150 + 150 = 0 150 + -100x + -4x2 = 0 + 100x + -100x + 4x2 + -4x2 150 + -100x + -4x2 = 100x + -100x + 4x2 + -4x2 Combine like terms: 100x + -100x = 0 150 + -100x + -4x2 = 0 + 4x2 + -4x2 150 + -100x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 150 + -100x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(75 + -50x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + -50x + -2x2)' equal to zero and attempt to solve: Simplifying 75 + -50x + -2x2 = 0 Solving 75 + -50x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -37.5 + 25x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + 25x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + 25x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + 25x + x2 = 0 + 37.5 25x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 25x + x2 = 37.5 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 37.5 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 37.5 + 156.25 Combine like terms: 37.5 + 156.25 = 193.75 156.25 + 25x + x2 = 193.75 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 193.75 Calculate the square root of the right side: 13.919410907 Break this problem into two subproblems by setting (x + 12.5) equal to 13.919410907 and -13.919410907.Subproblem 1
x + 12.5 = 13.919410907 Simplifying x + 12.5 = 13.919410907 Reorder the terms: 12.5 + x = 13.919410907 Solving 12.5 + x = 13.919410907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 13.919410907 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 13.919410907 + -12.5 x = 13.919410907 + -12.5 Combine like terms: 13.919410907 + -12.5 = 1.419410907 x = 1.419410907 Simplifying x = 1.419410907Subproblem 2
x + 12.5 = -13.919410907 Simplifying x + 12.5 = -13.919410907 Reorder the terms: 12.5 + x = -13.919410907 Solving 12.5 + x = -13.919410907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -13.919410907 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -13.919410907 + -12.5 x = -13.919410907 + -12.5 Combine like terms: -13.919410907 + -12.5 = -26.419410907 x = -26.419410907 Simplifying x = -26.419410907Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.419410907, -26.419410907}Solution
x = {1.419410907, -26.419410907}
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