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Simplifying x = -5x2 + 790x + -400 Reorder the terms: x = -400 + 790x + -5x2 Solving x = -400 + 790x + -5x2 Solving for variable 'x'. Reorder the terms: 400 + x + -790x + 5x2 = -400 + 790x + -5x2 + 400 + -790x + 5x2 Combine like terms: x + -790x = -789x 400 + -789x + 5x2 = -400 + 790x + -5x2 + 400 + -790x + 5x2 Reorder the terms: 400 + -789x + 5x2 = -400 + 400 + 790x + -790x + -5x2 + 5x2 Combine like terms: -400 + 400 = 0 400 + -789x + 5x2 = 0 + 790x + -790x + -5x2 + 5x2 400 + -789x + 5x2 = 790x + -790x + -5x2 + 5x2 Combine like terms: 790x + -790x = 0 400 + -789x + 5x2 = 0 + -5x2 + 5x2 400 + -789x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 400 + -789x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 80 + -157.8x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -157.8x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -157.8x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -157.8x + x2 = 0 + -80 -157.8x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -157.8x + x2 = -80 The x term is -157.8x. Take half its coefficient (-78.9). Square it (6225.21) and add it to both sides. Add '6225.21' to each side of the equation. -157.8x + 6225.21 + x2 = -80 + 6225.21 Reorder the terms: 6225.21 + -157.8x + x2 = -80 + 6225.21 Combine like terms: -80 + 6225.21 = 6145.21 6225.21 + -157.8x + x2 = 6145.21 Factor a perfect square on the left side: (x + -78.9)(x + -78.9) = 6145.21 Calculate the square root of the right side: 78.391389833 Break this problem into two subproblems by setting (x + -78.9) equal to 78.391389833 and -78.391389833.Subproblem 1
x + -78.9 = 78.391389833 Simplifying x + -78.9 = 78.391389833 Reorder the terms: -78.9 + x = 78.391389833 Solving -78.9 + x = 78.391389833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '78.9' to each side of the equation. -78.9 + 78.9 + x = 78.391389833 + 78.9 Combine like terms: -78.9 + 78.9 = 0.0 0.0 + x = 78.391389833 + 78.9 x = 78.391389833 + 78.9 Combine like terms: 78.391389833 + 78.9 = 157.291389833 x = 157.291389833 Simplifying x = 157.291389833Subproblem 2
x + -78.9 = -78.391389833 Simplifying x + -78.9 = -78.391389833 Reorder the terms: -78.9 + x = -78.391389833 Solving -78.9 + x = -78.391389833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '78.9' to each side of the equation. -78.9 + 78.9 + x = -78.391389833 + 78.9 Combine like terms: -78.9 + 78.9 = 0.0 0.0 + x = -78.391389833 + 78.9 x = -78.391389833 + 78.9 Combine like terms: -78.391389833 + 78.9 = 0.508610167 x = 0.508610167 Simplifying x = 0.508610167Solution
The solution to the problem is based on the solutions from the subproblems. x = {157.291389833, 0.508610167}
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