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Simplifying -5x2 + 40x + 23 = 0 Reorder the terms: 23 + 40x + -5x2 = 0 Solving 23 + 40x + -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'. -4.6 + -8x + x2 = 0 Move the constant term to the right: Add '4.6' to each side of the equation. -4.6 + -8x + 4.6 + x2 = 0 + 4.6 Reorder the terms: -4.6 + 4.6 + -8x + x2 = 0 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + -8x + x2 = 0 + 4.6 -8x + x2 = 0 + 4.6 Combine like terms: 0 + 4.6 = 4.6 -8x + x2 = 4.6 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 4.6 + 16 Reorder the terms: 16 + -8x + x2 = 4.6 + 16 Combine like terms: 4.6 + 16 = 20.6 16 + -8x + x2 = 20.6 Factor a perfect square on the left side: (x + -4)(x + -4) = 20.6 Calculate the square root of the right side: 4.538722287 Break this problem into two subproblems by setting (x + -4) equal to 4.538722287 and -4.538722287.Subproblem 1
x + -4 = 4.538722287 Simplifying x + -4 = 4.538722287 Reorder the terms: -4 + x = 4.538722287 Solving -4 + x = 4.538722287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.538722287 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.538722287 + 4 x = 4.538722287 + 4 Combine like terms: 4.538722287 + 4 = 8.538722287 x = 8.538722287 Simplifying x = 8.538722287Subproblem 2
x + -4 = -4.538722287 Simplifying x + -4 = -4.538722287 Reorder the terms: -4 + x = -4.538722287 Solving -4 + x = -4.538722287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.538722287 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.538722287 + 4 x = -4.538722287 + 4 Combine like terms: -4.538722287 + 4 = -0.538722287 x = -0.538722287 Simplifying x = -0.538722287Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.538722287, -0.538722287}
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