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Simplifying 7x = 13x2 + -8 Reorder the terms: 7x = -8 + 13x2 Solving 7x = -8 + 13x2 Solving for variable 'x'. Reorder the terms: 8 + 7x + -13x2 = -8 + 13x2 + 8 + -13x2 Reorder the terms: 8 + 7x + -13x2 = -8 + 8 + 13x2 + -13x2 Combine like terms: -8 + 8 = 0 8 + 7x + -13x2 = 0 + 13x2 + -13x2 8 + 7x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 8 + 7x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.6153846154 + -0.5384615385x + x2 = 0 Move the constant term to the right: Add '0.6153846154' to each side of the equation. -0.6153846154 + -0.5384615385x + 0.6153846154 + x2 = 0 + 0.6153846154 Reorder the terms: -0.6153846154 + 0.6153846154 + -0.5384615385x + x2 = 0 + 0.6153846154 Combine like terms: -0.6153846154 + 0.6153846154 = 0.0000000000 0.0000000000 + -0.5384615385x + x2 = 0 + 0.6153846154 -0.5384615385x + x2 = 0 + 0.6153846154 Combine like terms: 0 + 0.6153846154 = 0.6153846154 -0.5384615385x + x2 = 0.6153846154 The x term is -0.5384615385x. Take half its coefficient (-0.2692307693). Square it (0.07248520714) and add it to both sides. Add '0.07248520714' to each side of the equation. -0.5384615385x + 0.07248520714 + x2 = 0.6153846154 + 0.07248520714 Reorder the terms: 0.07248520714 + -0.5384615385x + x2 = 0.6153846154 + 0.07248520714 Combine like terms: 0.6153846154 + 0.07248520714 = 0.68786982254 0.07248520714 + -0.5384615385x + x2 = 0.68786982254 Factor a perfect square on the left side: (x + -0.2692307693)(x + -0.2692307693) = 0.68786982254 Calculate the square root of the right side: 0.829379179 Break this problem into two subproblems by setting (x + -0.2692307693) equal to 0.829379179 and -0.829379179.Subproblem 1
x + -0.2692307693 = 0.829379179 Simplifying x + -0.2692307693 = 0.829379179 Reorder the terms: -0.2692307693 + x = 0.829379179 Solving -0.2692307693 + x = 0.829379179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2692307693' to each side of the equation. -0.2692307693 + 0.2692307693 + x = 0.829379179 + 0.2692307693 Combine like terms: -0.2692307693 + 0.2692307693 = 0.0000000000 0.0000000000 + x = 0.829379179 + 0.2692307693 x = 0.829379179 + 0.2692307693 Combine like terms: 0.829379179 + 0.2692307693 = 1.0986099483 x = 1.0986099483 Simplifying x = 1.0986099483Subproblem 2
x + -0.2692307693 = -0.829379179 Simplifying x + -0.2692307693 = -0.829379179 Reorder the terms: -0.2692307693 + x = -0.829379179 Solving -0.2692307693 + x = -0.829379179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2692307693' to each side of the equation. -0.2692307693 + 0.2692307693 + x = -0.829379179 + 0.2692307693 Combine like terms: -0.2692307693 + 0.2692307693 = 0.0000000000 0.0000000000 + x = -0.829379179 + 0.2692307693 x = -0.829379179 + 0.2692307693 Combine like terms: -0.829379179 + 0.2692307693 = -0.5601484097 x = -0.5601484097 Simplifying x = -0.5601484097Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0986099483, -0.5601484097}
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