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Simplifying 0 = -5x2 + 10x + 50 Reorder the terms: 0 = 50 + 10x + -5x2 Solving 0 = 50 + 10x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + -10x + 5x2 = 50 + 10x + -5x2 + -50 + -10x + 5x2 Reorder the terms: -50 + -10x + 5x2 = 50 + -50 + 10x + -10x + -5x2 + 5x2 Combine like terms: 50 + -50 = 0 -50 + -10x + 5x2 = 0 + 10x + -10x + -5x2 + 5x2 -50 + -10x + 5x2 = 10x + -10x + -5x2 + 5x2 Combine like terms: 10x + -10x = 0 -50 + -10x + 5x2 = 0 + -5x2 + 5x2 -50 + -10x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -50 + -10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-10 + -2x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-10 + -2x + x2)' equal to zero and attempt to solve: Simplifying -10 + -2x + x2 = 0 Solving -10 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -2x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -2x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2x + x2 = 0 + 10 -2x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2x + x2 = 10 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 = 10 + 1 Reorder the terms: 1 + -2x + x2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + -2x + x2 = 11 Factor a perfect square on the left side: (x + -1)(x + -1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -1) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -1 = 3.31662479 Simplifying x + -1 = 3.31662479 Reorder the terms: -1 + x = 3.31662479 Solving -1 + x = 3.31662479 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 = 3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.31662479 + 1 x = 3.31662479 + 1 Combine like terms: 3.31662479 + 1 = 4.31662479 x = 4.31662479 Simplifying x = 4.31662479Subproblem 2
x + -1 = -3.31662479 Simplifying x + -1 = -3.31662479 Reorder the terms: -1 + x = -3.31662479 Solving -1 + x = -3.31662479 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 = -3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.31662479 + 1 x = -3.31662479 + 1 Combine like terms: -3.31662479 + 1 = -2.31662479 x = -2.31662479 Simplifying x = -2.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.31662479, -2.31662479}Solution
x = {4.31662479, -2.31662479}
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