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Simplifying 5x2 + 8x + -1760 = 0 Reorder the terms: -1760 + 8x + 5x2 = 0 Solving -1760 + 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'. -352 + 1.6x + x2 = 0 Move the constant term to the right: Add '352' to each side of the equation. -352 + 1.6x + 352 + x2 = 0 + 352 Reorder the terms: -352 + 352 + 1.6x + x2 = 0 + 352 Combine like terms: -352 + 352 = 0 0 + 1.6x + x2 = 0 + 352 1.6x + x2 = 0 + 352 Combine like terms: 0 + 352 = 352 1.6x + x2 = 352 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 = 352 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 352 + 0.64 Combine like terms: 352 + 0.64 = 352.64 0.64 + 1.6x + x2 = 352.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 352.64 Calculate the square root of the right side: 18.778711351 Break this problem into two subproblems by setting (x + 0.8) equal to 18.778711351 and -18.778711351.Subproblem 1
x + 0.8 = 18.778711351 Simplifying x + 0.8 = 18.778711351 Reorder the terms: 0.8 + x = 18.778711351 Solving 0.8 + x = 18.778711351 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 = 18.778711351 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 18.778711351 + -0.8 x = 18.778711351 + -0.8 Combine like terms: 18.778711351 + -0.8 = 17.978711351 x = 17.978711351 Simplifying x = 17.978711351Subproblem 2
x + 0.8 = -18.778711351 Simplifying x + 0.8 = -18.778711351 Reorder the terms: 0.8 + x = -18.778711351 Solving 0.8 + x = -18.778711351 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 = -18.778711351 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -18.778711351 + -0.8 x = -18.778711351 + -0.8 Combine like terms: -18.778711351 + -0.8 = -19.578711351 x = -19.578711351 Simplifying x = -19.578711351Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.978711351, -19.578711351}
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