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Simplifying 5x2 + 4x = 170 Reorder the terms: 4x + 5x2 = 170 Solving 4x + 5x2 = 170 Solving for variable 'x'. Reorder the terms: -170 + 4x + 5x2 = 170 + -170 Combine like terms: 170 + -170 = 0 -170 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -34 + 0.8x + x2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + 0.8x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 0.8x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 0.8x + x2 = 0 + 34 0.8x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 0.8x + x2 = 34 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 = 34 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 34 + 0.16 Combine like terms: 34 + 0.16 = 34.16 0.16 + 0.8x + x2 = 34.16 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 34.16 Calculate the square root of the right side: 5.844655678 Break this problem into two subproblems by setting (x + 0.4) equal to 5.844655678 and -5.844655678.Subproblem 1
x + 0.4 = 5.844655678 Simplifying x + 0.4 = 5.844655678 Reorder the terms: 0.4 + x = 5.844655678 Solving 0.4 + x = 5.844655678 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 = 5.844655678 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 5.844655678 + -0.4 x = 5.844655678 + -0.4 Combine like terms: 5.844655678 + -0.4 = 5.444655678 x = 5.444655678 Simplifying x = 5.444655678Subproblem 2
x + 0.4 = -5.844655678 Simplifying x + 0.4 = -5.844655678 Reorder the terms: 0.4 + x = -5.844655678 Solving 0.4 + x = -5.844655678 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 = -5.844655678 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -5.844655678 + -0.4 x = -5.844655678 + -0.4 Combine like terms: -5.844655678 + -0.4 = -6.244655678 x = -6.244655678 Simplifying x = -6.244655678Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.444655678, -6.244655678}
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