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Simplifying 800 = 2x2 + x Reorder the terms: 800 = x + 2x2 Solving 800 = x + 2x2 Solving for variable 'x'. Reorder the terms: 800 + -1x + -2x2 = x + -1x + 2x2 + -2x2 Combine like terms: x + -1x = 0 800 + -1x + -2x2 = 0 + 2x2 + -2x2 800 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 800 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -400 + 0.5x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + 0.5x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 0.5x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 0.5x + x2 = 0 + 400 0.5x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 0.5x + x2 = 400 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 400 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 400 + 0.0625 Combine like terms: 400 + 0.0625 = 400.0625 0.0625 + 0.5x + x2 = 400.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 400.0625 Calculate the square root of the right side: 20.001562439 Break this problem into two subproblems by setting (x + 0.25) equal to 20.001562439 and -20.001562439.Subproblem 1
x + 0.25 = 20.001562439 Simplifying x + 0.25 = 20.001562439 Reorder the terms: 0.25 + x = 20.001562439 Solving 0.25 + x = 20.001562439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 20.001562439 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 20.001562439 + -0.25 x = 20.001562439 + -0.25 Combine like terms: 20.001562439 + -0.25 = 19.751562439 x = 19.751562439 Simplifying x = 19.751562439Subproblem 2
x + 0.25 = -20.001562439 Simplifying x + 0.25 = -20.001562439 Reorder the terms: 0.25 + x = -20.001562439 Solving 0.25 + x = -20.001562439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -20.001562439 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -20.001562439 + -0.25 x = -20.001562439 + -0.25 Combine like terms: -20.001562439 + -0.25 = -20.251562439 x = -20.251562439 Simplifying x = -20.251562439Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.751562439, -20.251562439}
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