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Simplifying 158 + -4x = x2 + -5x Reorder the terms: 158 + -4x = -5x + x2 Solving 158 + -4x = -5x + x2 Solving for variable 'x'. Combine like terms: -4x + 5x = 1x 158 + 1x + -1x2 = -5x + x2 + 5x + -1x2 Reorder the terms: 158 + 1x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 158 + 1x + -1x2 = 0 + x2 + -1x2 158 + 1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 158 + 1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -158 + -1x + x2 = 0 Move the constant term to the right: Add '158' to each side of the equation. -158 + -1x + 158 + x2 = 0 + 158 Reorder the terms: -158 + 158 + -1x + x2 = 0 + 158 Combine like terms: -158 + 158 = 0 0 + -1x + x2 = 0 + 158 -1x + x2 = 0 + 158 Combine like terms: 0 + 158 = 158 -1x + x2 = 158 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 158 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 158 + 0.25 Combine like terms: 158 + 0.25 = 158.25 0.25 + -1x + x2 = 158.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 158.25 Calculate the square root of the right side: 12.579745625 Break this problem into two subproblems by setting (x + -0.5) equal to 12.579745625 and -12.579745625.Subproblem 1
x + -0.5 = 12.579745625 Simplifying x + -0.5 = 12.579745625 Reorder the terms: -0.5 + x = 12.579745625 Solving -0.5 + x = 12.579745625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 12.579745625 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 12.579745625 + 0.5 x = 12.579745625 + 0.5 Combine like terms: 12.579745625 + 0.5 = 13.079745625 x = 13.079745625 Simplifying x = 13.079745625Subproblem 2
x + -0.5 = -12.579745625 Simplifying x + -0.5 = -12.579745625 Reorder the terms: -0.5 + x = -12.579745625 Solving -0.5 + x = -12.579745625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -12.579745625 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -12.579745625 + 0.5 x = -12.579745625 + 0.5 Combine like terms: -12.579745625 + 0.5 = -12.079745625 x = -12.079745625 Simplifying x = -12.079745625Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.079745625, -12.079745625}
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