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Simplifying -8x2 + -40x + 3 = 0 Reorder the terms: 3 + -40x + -8x2 = 0 Solving 3 + -40x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + 5x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 5x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 5x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 5x + x2 = 0 + 0.375 5x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 5x + x2 = 0.375 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 0.375 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.375 + 6.25 Combine like terms: 0.375 + 6.25 = 6.625 6.25 + 5x + x2 = 6.625 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.625 Calculate the square root of the right side: 2.573907535 Break this problem into two subproblems by setting (x + 2.5) equal to 2.573907535 and -2.573907535.Subproblem 1
x + 2.5 = 2.573907535 Simplifying x + 2.5 = 2.573907535 Reorder the terms: 2.5 + x = 2.573907535 Solving 2.5 + x = 2.573907535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.573907535 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.573907535 + -2.5 x = 2.573907535 + -2.5 Combine like terms: 2.573907535 + -2.5 = 0.073907535 x = 0.073907535 Simplifying x = 0.073907535Subproblem 2
x + 2.5 = -2.573907535 Simplifying x + 2.5 = -2.573907535 Reorder the terms: 2.5 + x = -2.573907535 Solving 2.5 + x = -2.573907535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.573907535 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.573907535 + -2.5 x = -2.573907535 + -2.5 Combine like terms: -2.573907535 + -2.5 = -5.073907535 x = -5.073907535 Simplifying x = -5.073907535Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.073907535, -5.073907535}
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