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Simplifying 98x + -4x2 = 150 Solving 98x + -4x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 98x + -4x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 98x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 49x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + 49x + -2x2)' equal to zero and attempt to solve: Simplifying -75 + 49x + -2x2 = 0 Solving -75 + 49x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 37.5 + -24.5x + x2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -24.5x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -24.5x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -24.5x + x2 = 0 + -37.5 -24.5x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -24.5x + x2 = -37.5 The x term is -24.5x. Take half its coefficient (-12.25). Square it (150.0625) and add it to both sides. Add '150.0625' to each side of the equation. -24.5x + 150.0625 + x2 = -37.5 + 150.0625 Reorder the terms: 150.0625 + -24.5x + x2 = -37.5 + 150.0625 Combine like terms: -37.5 + 150.0625 = 112.5625 150.0625 + -24.5x + x2 = 112.5625 Factor a perfect square on the left side: (x + -12.25)(x + -12.25) = 112.5625 Calculate the square root of the right side: 10.609547587 Break this problem into two subproblems by setting (x + -12.25) equal to 10.609547587 and -10.609547587.Subproblem 1
x + -12.25 = 10.609547587 Simplifying x + -12.25 = 10.609547587 Reorder the terms: -12.25 + x = 10.609547587 Solving -12.25 + x = 10.609547587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.25' to each side of the equation. -12.25 + 12.25 + x = 10.609547587 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + x = 10.609547587 + 12.25 x = 10.609547587 + 12.25 Combine like terms: 10.609547587 + 12.25 = 22.859547587 x = 22.859547587 Simplifying x = 22.859547587Subproblem 2
x + -12.25 = -10.609547587 Simplifying x + -12.25 = -10.609547587 Reorder the terms: -12.25 + x = -10.609547587 Solving -12.25 + x = -10.609547587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.25' to each side of the equation. -12.25 + 12.25 + x = -10.609547587 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + x = -10.609547587 + 12.25 x = -10.609547587 + 12.25 Combine like terms: -10.609547587 + 12.25 = 1.640452413 x = 1.640452413 Simplifying x = 1.640452413Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.859547587, 1.640452413}Solution
x = {22.859547587, 1.640452413}
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