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Simplifying 4x2 + 5x + -85 = 0 Reorder the terms: -85 + 5x + 4x2 = 0 Solving -85 + 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'. -21.25 + 1.25x + x2 = 0 Move the constant term to the right: Add '21.25' to each side of the equation. -21.25 + 1.25x + 21.25 + x2 = 0 + 21.25 Reorder the terms: -21.25 + 21.25 + 1.25x + x2 = 0 + 21.25 Combine like terms: -21.25 + 21.25 = 0.00 0.00 + 1.25x + x2 = 0 + 21.25 1.25x + x2 = 0 + 21.25 Combine like terms: 0 + 21.25 = 21.25 1.25x + x2 = 21.25 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 = 21.25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 21.25 + 0.390625 Combine like terms: 21.25 + 0.390625 = 21.640625 0.390625 + 1.25x + x2 = 21.640625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 21.640625 Calculate the square root of the right side: 4.651948516 Break this problem into two subproblems by setting (x + 0.625) equal to 4.651948516 and -4.651948516.Subproblem 1
x + 0.625 = 4.651948516 Simplifying x + 0.625 = 4.651948516 Reorder the terms: 0.625 + x = 4.651948516 Solving 0.625 + x = 4.651948516 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 = 4.651948516 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 4.651948516 + -0.625 x = 4.651948516 + -0.625 Combine like terms: 4.651948516 + -0.625 = 4.026948516 x = 4.026948516 Simplifying x = 4.026948516Subproblem 2
x + 0.625 = -4.651948516 Simplifying x + 0.625 = -4.651948516 Reorder the terms: 0.625 + x = -4.651948516 Solving 0.625 + x = -4.651948516 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 = -4.651948516 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -4.651948516 + -0.625 x = -4.651948516 + -0.625 Combine like terms: -4.651948516 + -0.625 = -5.276948516 x = -5.276948516 Simplifying x = -5.276948516Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.026948516, -5.276948516}
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