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Simplifying 5x2 + 8x = 19 Reorder the terms: 8x + 5x2 = 19 Solving 8x + 5x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + 8x + 5x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.8 + 1.6x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + 1.6x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + 1.6x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + 1.6x + x2 = 0 + 3.8 1.6x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 1.6x + x2 = 3.8 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 3.8 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 3.8 + 0.64 Combine like terms: 3.8 + 0.64 = 4.44 0.64 + 1.6x + x2 = 4.44 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 4.44 Calculate the square root of the right side: 2.107130751 Break this problem into two subproblems by setting (x + 0.8) equal to 2.107130751 and -2.107130751.Subproblem 1
x + 0.8 = 2.107130751 Simplifying x + 0.8 = 2.107130751 Reorder the terms: 0.8 + x = 2.107130751 Solving 0.8 + x = 2.107130751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 2.107130751 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 2.107130751 + -0.8 x = 2.107130751 + -0.8 Combine like terms: 2.107130751 + -0.8 = 1.307130751 x = 1.307130751 Simplifying x = 1.307130751Subproblem 2
x + 0.8 = -2.107130751 Simplifying x + 0.8 = -2.107130751 Reorder the terms: 0.8 + x = -2.107130751 Solving 0.8 + x = -2.107130751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -2.107130751 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -2.107130751 + -0.8 x = -2.107130751 + -0.8 Combine like terms: -2.107130751 + -0.8 = -2.907130751 x = -2.907130751 Simplifying x = -2.907130751Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.307130751, -2.907130751}
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