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Simplifying 4x2 + -5x + -400 = 0 Reorder the terms: -400 + -5x + 4x2 = 0 Solving -400 + -5x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -100 + -1.25x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -1.25x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -1.25x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -1.25x + x2 = 0 + 100 -1.25x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -1.25x + x2 = 100 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 100 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 100 + 0.390625 Combine like terms: 100 + 0.390625 = 100.390625 0.390625 + -1.25x + x2 = 100.390625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 100.390625 Calculate the square root of the right side: 10.019512214 Break this problem into two subproblems by setting (x + -0.625) equal to 10.019512214 and -10.019512214.Subproblem 1
x + -0.625 = 10.019512214 Simplifying x + -0.625 = 10.019512214 Reorder the terms: -0.625 + x = 10.019512214 Solving -0.625 + x = 10.019512214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 10.019512214 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 10.019512214 + 0.625 x = 10.019512214 + 0.625 Combine like terms: 10.019512214 + 0.625 = 10.644512214 x = 10.644512214 Simplifying x = 10.644512214Subproblem 2
x + -0.625 = -10.019512214 Simplifying x + -0.625 = -10.019512214 Reorder the terms: -0.625 + x = -10.019512214 Solving -0.625 + x = -10.019512214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -10.019512214 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -10.019512214 + 0.625 x = -10.019512214 + 0.625 Combine like terms: -10.019512214 + 0.625 = -9.394512214 x = -9.394512214 Simplifying x = -9.394512214Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.644512214, -9.394512214}
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