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Simplifying 5x2 + 8x + -52 = 0 Reorder the terms: -52 + 8x + 5x2 = 0 Solving -52 + 8x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.4 + 1.6x + x2 = 0 Move the constant term to the right: Add '10.4' to each side of the equation. -10.4 + 1.6x + 10.4 + x2 = 0 + 10.4 Reorder the terms: -10.4 + 10.4 + 1.6x + x2 = 0 + 10.4 Combine like terms: -10.4 + 10.4 = 0.0 0.0 + 1.6x + x2 = 0 + 10.4 1.6x + x2 = 0 + 10.4 Combine like terms: 0 + 10.4 = 10.4 1.6x + x2 = 10.4 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 = 10.4 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 10.4 + 0.64 Combine like terms: 10.4 + 0.64 = 11.04 0.64 + 1.6x + x2 = 11.04 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 11.04 Calculate the square root of the right side: 3.322649545 Break this problem into two subproblems by setting (x + 0.8) equal to 3.322649545 and -3.322649545.Subproblem 1
x + 0.8 = 3.322649545 Simplifying x + 0.8 = 3.322649545 Reorder the terms: 0.8 + x = 3.322649545 Solving 0.8 + x = 3.322649545 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 = 3.322649545 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 3.322649545 + -0.8 x = 3.322649545 + -0.8 Combine like terms: 3.322649545 + -0.8 = 2.522649545 x = 2.522649545 Simplifying x = 2.522649545Subproblem 2
x + 0.8 = -3.322649545 Simplifying x + 0.8 = -3.322649545 Reorder the terms: 0.8 + x = -3.322649545 Solving 0.8 + x = -3.322649545 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 = -3.322649545 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -3.322649545 + -0.8 x = -3.322649545 + -0.8 Combine like terms: -3.322649545 + -0.8 = -4.122649545 x = -4.122649545 Simplifying x = -4.122649545Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.522649545, -4.122649545}
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