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Simplifying 13x2 = 16x + 5 Reorder the terms: 13x2 = 5 + 16x Solving 13x2 = 5 + 16x Solving for variable 'x'. Reorder the terms: -5 + -16x + 13x2 = 5 + 16x + -5 + -16x Reorder the terms: -5 + -16x + 13x2 = 5 + -5 + 16x + -16x Combine like terms: 5 + -5 = 0 -5 + -16x + 13x2 = 0 + 16x + -16x -5 + -16x + 13x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -5 + -16x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.3846153846 + -1.230769231x + x2 = 0 Move the constant term to the right: Add '0.3846153846' to each side of the equation. -0.3846153846 + -1.230769231x + 0.3846153846 + x2 = 0 + 0.3846153846 Reorder the terms: -0.3846153846 + 0.3846153846 + -1.230769231x + x2 = 0 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + -1.230769231x + x2 = 0 + 0.3846153846 -1.230769231x + x2 = 0 + 0.3846153846 Combine like terms: 0 + 0.3846153846 = 0.3846153846 -1.230769231x + x2 = 0.3846153846 The x term is -1.230769231x. Take half its coefficient (-0.6153846155). Square it (0.3786982250) and add it to both sides. Add '0.3786982250' to each side of the equation. -1.230769231x + 0.3786982250 + x2 = 0.3846153846 + 0.3786982250 Reorder the terms: 0.3786982250 + -1.230769231x + x2 = 0.3846153846 + 0.3786982250 Combine like terms: 0.3846153846 + 0.3786982250 = 0.7633136096 0.3786982250 + -1.230769231x + x2 = 0.7633136096 Factor a perfect square on the left side: (x + -0.6153846155)(x + -0.6153846155) = 0.7633136096 Calculate the square root of the right side: 0.873678207 Break this problem into two subproblems by setting (x + -0.6153846155) equal to 0.873678207 and -0.873678207.Subproblem 1
x + -0.6153846155 = 0.873678207 Simplifying x + -0.6153846155 = 0.873678207 Reorder the terms: -0.6153846155 + x = 0.873678207 Solving -0.6153846155 + x = 0.873678207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6153846155' to each side of the equation. -0.6153846155 + 0.6153846155 + x = 0.873678207 + 0.6153846155 Combine like terms: -0.6153846155 + 0.6153846155 = 0.0000000000 0.0000000000 + x = 0.873678207 + 0.6153846155 x = 0.873678207 + 0.6153846155 Combine like terms: 0.873678207 + 0.6153846155 = 1.4890628225 x = 1.4890628225 Simplifying x = 1.4890628225Subproblem 2
x + -0.6153846155 = -0.873678207 Simplifying x + -0.6153846155 = -0.873678207 Reorder the terms: -0.6153846155 + x = -0.873678207 Solving -0.6153846155 + x = -0.873678207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6153846155' to each side of the equation. -0.6153846155 + 0.6153846155 + x = -0.873678207 + 0.6153846155 Combine like terms: -0.6153846155 + 0.6153846155 = 0.0000000000 0.0000000000 + x = -0.873678207 + 0.6153846155 x = -0.873678207 + 0.6153846155 Combine like terms: -0.873678207 + 0.6153846155 = -0.2582935915 x = -0.2582935915 Simplifying x = -0.2582935915Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4890628225, -0.2582935915}
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