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Simplifying 2x2 + -4x = 300 Reorder the terms: -4x + 2x2 = 300 Solving -4x + 2x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + -4x + 2x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-150 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-150 + -2x + x2)' equal to zero and attempt to solve: Simplifying -150 + -2x + x2 = 0 Solving -150 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + -2x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + -2x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -2x + x2 = 0 + 150 -2x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 -2x + x2 = 150 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 150 + 1 Reorder the terms: 1 + -2x + x2 = 150 + 1 Combine like terms: 150 + 1 = 151 1 + -2x + x2 = 151 Factor a perfect square on the left side: (x + -1)(x + -1) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + -1) equal to 12.288205727 and -12.288205727.Subproblem 1
x + -1 = 12.288205727 Simplifying x + -1 = 12.288205727 Reorder the terms: -1 + x = 12.288205727 Solving -1 + x = 12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 12.288205727 + 1 Combine like terms: -1 + 1 = 0 0 + x = 12.288205727 + 1 x = 12.288205727 + 1 Combine like terms: 12.288205727 + 1 = 13.288205727 x = 13.288205727 Simplifying x = 13.288205727Subproblem 2
x + -1 = -12.288205727 Simplifying x + -1 = -12.288205727 Reorder the terms: -1 + x = -12.288205727 Solving -1 + x = -12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -12.288205727 + 1 Combine like terms: -1 + 1 = 0 0 + x = -12.288205727 + 1 x = -12.288205727 + 1 Combine like terms: -12.288205727 + 1 = -11.288205727 x = -11.288205727 Simplifying x = -11.288205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.288205727, -11.288205727}Solution
x = {13.288205727, -11.288205727}
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