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Simplifying 5x2 + 28x + -1887 = 0 Reorder the terms: -1887 + 28x + 5x2 = 0 Solving -1887 + 28x + 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'. -377.4 + 5.6x + x2 = 0 Move the constant term to the right: Add '377.4' to each side of the equation. -377.4 + 5.6x + 377.4 + x2 = 0 + 377.4 Reorder the terms: -377.4 + 377.4 + 5.6x + x2 = 0 + 377.4 Combine like terms: -377.4 + 377.4 = 0.0 0.0 + 5.6x + x2 = 0 + 377.4 5.6x + x2 = 0 + 377.4 Combine like terms: 0 + 377.4 = 377.4 5.6x + x2 = 377.4 The x term is 5.6x. Take half its coefficient (2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. 5.6x + 7.84 + x2 = 377.4 + 7.84 Reorder the terms: 7.84 + 5.6x + x2 = 377.4 + 7.84 Combine like terms: 377.4 + 7.84 = 385.24 7.84 + 5.6x + x2 = 385.24 Factor a perfect square on the left side: (x + 2.8)(x + 2.8) = 385.24 Calculate the square root of the right side: 19.627531684 Break this problem into two subproblems by setting (x + 2.8) equal to 19.627531684 and -19.627531684.Subproblem 1
x + 2.8 = 19.627531684 Simplifying x + 2.8 = 19.627531684 Reorder the terms: 2.8 + x = 19.627531684 Solving 2.8 + x = 19.627531684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = 19.627531684 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = 19.627531684 + -2.8 x = 19.627531684 + -2.8 Combine like terms: 19.627531684 + -2.8 = 16.827531684 x = 16.827531684 Simplifying x = 16.827531684Subproblem 2
x + 2.8 = -19.627531684 Simplifying x + 2.8 = -19.627531684 Reorder the terms: 2.8 + x = -19.627531684 Solving 2.8 + x = -19.627531684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = -19.627531684 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = -19.627531684 + -2.8 x = -19.627531684 + -2.8 Combine like terms: -19.627531684 + -2.8 = -22.427531684 x = -22.427531684 Simplifying x = -22.427531684Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.827531684, -22.427531684}
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