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Simplifying -1.3x2 = 13x + -8 Reorder the terms: -1.3x2 = -8 + 13x Solving -1.3x2 = -8 + 13x Solving for variable 'x'. Reorder the terms: 8 + -13x + -1.3x2 = -8 + 13x + 8 + -13x Reorder the terms: 8 + -13x + -1.3x2 = -8 + 8 + 13x + -13x Combine like terms: -8 + 8 = 0 8 + -13x + -1.3x2 = 0 + 13x + -13x 8 + -13x + -1.3x2 = 13x + -13x Combine like terms: 13x + -13x = 0 8 + -13x + -1.3x2 = 0 Begin completing the square. Divide all terms by -1.3 the coefficient of the squared term: Divide each side by '-1.3'. -6.153846154 + 10x + x2 = 0 Move the constant term to the right: Add '6.153846154' to each side of the equation. -6.153846154 + 10x + 6.153846154 + x2 = 0 + 6.153846154 Reorder the terms: -6.153846154 + 6.153846154 + 10x + x2 = 0 + 6.153846154 Combine like terms: -6.153846154 + 6.153846154 = 0.000000000 0.000000000 + 10x + x2 = 0 + 6.153846154 10x + x2 = 0 + 6.153846154 Combine like terms: 0 + 6.153846154 = 6.153846154 10x + x2 = 6.153846154 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 6.153846154 + 25 Reorder the terms: 25 + 10x + x2 = 6.153846154 + 25 Combine like terms: 6.153846154 + 25 = 31.153846154 25 + 10x + x2 = 31.153846154 Factor a perfect square on the left side: (x + 5)(x + 5) = 31.153846154 Calculate the square root of the right side: 5.581563057 Break this problem into two subproblems by setting (x + 5) equal to 5.581563057 and -5.581563057.Subproblem 1
x + 5 = 5.581563057 Simplifying x + 5 = 5.581563057 Reorder the terms: 5 + x = 5.581563057 Solving 5 + x = 5.581563057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.581563057 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.581563057 + -5 x = 5.581563057 + -5 Combine like terms: 5.581563057 + -5 = 0.581563057 x = 0.581563057 Simplifying x = 0.581563057Subproblem 2
x + 5 = -5.581563057 Simplifying x + 5 = -5.581563057 Reorder the terms: 5 + x = -5.581563057 Solving 5 + x = -5.581563057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.581563057 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.581563057 + -5 x = -5.581563057 + -5 Combine like terms: -5.581563057 + -5 = -10.581563057 x = -10.581563057 Simplifying x = -10.581563057Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.581563057, -10.581563057}
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