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Simplifying 5x2 = -4x + 19 Reorder the terms: 5x2 = 19 + -4x Solving 5x2 = 19 + -4x Solving for variable 'x'. Reorder the terms: -19 + 4x + 5x2 = 19 + -4x + -19 + 4x Reorder the terms: -19 + 4x + 5x2 = 19 + -19 + -4x + 4x Combine like terms: 19 + -19 = 0 -19 + 4x + 5x2 = 0 + -4x + 4x -19 + 4x + 5x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -19 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.8 + 0.8x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + 0.8x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + 0.8x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + 0.8x + x2 = 0 + 3.8 0.8x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 0.8x + x2 = 3.8 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 3.8 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 3.8 + 0.16 Combine like terms: 3.8 + 0.16 = 3.96 0.16 + 0.8x + x2 = 3.96 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 3.96 Calculate the square root of the right side: 1.989974874 Break this problem into two subproblems by setting (x + 0.4) equal to 1.989974874 and -1.989974874.Subproblem 1
x + 0.4 = 1.989974874 Simplifying x + 0.4 = 1.989974874 Reorder the terms: 0.4 + x = 1.989974874 Solving 0.4 + x = 1.989974874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.989974874 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.989974874 + -0.4 x = 1.989974874 + -0.4 Combine like terms: 1.989974874 + -0.4 = 1.589974874 x = 1.589974874 Simplifying x = 1.589974874Subproblem 2
x + 0.4 = -1.989974874 Simplifying x + 0.4 = -1.989974874 Reorder the terms: 0.4 + x = -1.989974874 Solving 0.4 + x = -1.989974874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.989974874 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.989974874 + -0.4 x = -1.989974874 + -0.4 Combine like terms: -1.989974874 + -0.4 = -2.389974874 x = -2.389974874 Simplifying x = -2.389974874Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.589974874, -2.389974874}
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