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Simplifying 4x2 + 12x + -7x + -64 = 0 Reorder the terms: -64 + 12x + -7x + 4x2 = 0 Combine like terms: 12x + -7x = 5x -64 + 5x + 4x2 = 0 Solving -64 + 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'. -16 + 1.25x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 1.25x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 1.25x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 1.25x + x2 = 0 + 16 1.25x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 1.25x + x2 = 16 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 = 16 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 16 + 0.390625 Combine like terms: 16 + 0.390625 = 16.390625 0.390625 + 1.25x + x2 = 16.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 16.390625 Calculate the square root of the right side: 4.048533685 Break this problem into two subproblems by setting (x + 0.625) equal to 4.048533685 and -4.048533685.Subproblem 1
x + 0.625 = 4.048533685 Simplifying x + 0.625 = 4.048533685 Reorder the terms: 0.625 + x = 4.048533685 Solving 0.625 + x = 4.048533685 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 = 4.048533685 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 4.048533685 + -0.625 x = 4.048533685 + -0.625 Combine like terms: 4.048533685 + -0.625 = 3.423533685 x = 3.423533685 Simplifying x = 3.423533685Subproblem 2
x + 0.625 = -4.048533685 Simplifying x + 0.625 = -4.048533685 Reorder the terms: 0.625 + x = -4.048533685 Solving 0.625 + x = -4.048533685 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 = -4.048533685 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -4.048533685 + -0.625 x = -4.048533685 + -0.625 Combine like terms: -4.048533685 + -0.625 = -4.673533685 x = -4.673533685 Simplifying x = -4.673533685Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.423533685, -4.673533685}
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