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Simplifying 4x2 + 5x = 80 Reorder the terms: 5x + 4x2 = 80 Solving 5x + 4x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 5x + 4x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -20 + 1.25x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 1.25x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 1.25x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 1.25x + x2 = 0 + 20 1.25x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 1.25x + x2 = 20 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 = 20 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 20 + 0.390625 Combine like terms: 20 + 0.390625 = 20.390625 0.390625 + 1.25x + x2 = 20.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 20.390625 Calculate the square root of the right side: 4.515597967 Break this problem into two subproblems by setting (x + 0.625) equal to 4.515597967 and -4.515597967.Subproblem 1
x + 0.625 = 4.515597967 Simplifying x + 0.625 = 4.515597967 Reorder the terms: 0.625 + x = 4.515597967 Solving 0.625 + x = 4.515597967 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 = 4.515597967 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 4.515597967 + -0.625 x = 4.515597967 + -0.625 Combine like terms: 4.515597967 + -0.625 = 3.890597967 x = 3.890597967 Simplifying x = 3.890597967Subproblem 2
x + 0.625 = -4.515597967 Simplifying x + 0.625 = -4.515597967 Reorder the terms: 0.625 + x = -4.515597967 Solving 0.625 + x = -4.515597967 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 = -4.515597967 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -4.515597967 + -0.625 x = -4.515597967 + -0.625 Combine like terms: -4.515597967 + -0.625 = -5.140597967 x = -5.140597967 Simplifying x = -5.140597967Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.890597967, -5.140597967}
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