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Simplifying x + -13x2 + 22 = 0 Reorder the terms: 22 + x + -13x2 = 0 Solving 22 + x + -13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -1.692307692 + -0.07692307692x + x2 = 0 Move the constant term to the right: Add '1.692307692' to each side of the equation. -1.692307692 + -0.07692307692x + 1.692307692 + x2 = 0 + 1.692307692 Reorder the terms: -1.692307692 + 1.692307692 + -0.07692307692x + x2 = 0 + 1.692307692 Combine like terms: -1.692307692 + 1.692307692 = 0.000000000 0.000000000 + -0.07692307692x + x2 = 0 + 1.692307692 -0.07692307692x + x2 = 0 + 1.692307692 Combine like terms: 0 + 1.692307692 = 1.692307692 -0.07692307692x + x2 = 1.692307692 The x term is x. 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. -0.07692307692x + 0.25 + x2 = 1.692307692 + 0.25 Reorder the terms: 0.25 + -0.07692307692x + x2 = 1.692307692 + 0.25 Combine like terms: 1.692307692 + 0.25 = 1.942307692 0.25 + -0.07692307692x + x2 = 1.942307692 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.942307692 Calculate the square root of the right side: 1.393666995 Break this problem into two subproblems by setting (x + 0.5) equal to 1.393666995 and -1.393666995.Subproblem 1
x + 0.5 = 1.393666995 Simplifying x + 0.5 = 1.393666995 Reorder the terms: 0.5 + x = 1.393666995 Solving 0.5 + x = 1.393666995 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 = 1.393666995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.393666995 + -0.5 x = 1.393666995 + -0.5 Combine like terms: 1.393666995 + -0.5 = 0.893666995 x = 0.893666995 Simplifying x = 0.893666995Subproblem 2
x + 0.5 = -1.393666995 Simplifying x + 0.5 = -1.393666995 Reorder the terms: 0.5 + x = -1.393666995 Solving 0.5 + x = -1.393666995 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 = -1.393666995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.393666995 + -0.5 x = -1.393666995 + -0.5 Combine like terms: -1.393666995 + -0.5 = -1.893666995 x = -1.893666995 Simplifying x = -1.893666995Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.893666995, -1.893666995}
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