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Simplifying 2x2 + -3x + -64 = 0 Reorder the terms: -64 + -3x + 2x2 = 0 Solving -64 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -32 + -1.5x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -1.5x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -1.5x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -1.5x + x2 = 0 + 32 -1.5x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -1.5x + x2 = 32 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 32 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 32 + 0.5625 Combine like terms: 32 + 0.5625 = 32.5625 0.5625 + -1.5x + x2 = 32.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 32.5625 Calculate the square root of the right side: 5.706356105 Break this problem into two subproblems by setting (x + -0.75) equal to 5.706356105 and -5.706356105.Subproblem 1
x + -0.75 = 5.706356105 Simplifying x + -0.75 = 5.706356105 Reorder the terms: -0.75 + x = 5.706356105 Solving -0.75 + x = 5.706356105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 5.706356105 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 5.706356105 + 0.75 x = 5.706356105 + 0.75 Combine like terms: 5.706356105 + 0.75 = 6.456356105 x = 6.456356105 Simplifying x = 6.456356105Subproblem 2
x + -0.75 = -5.706356105 Simplifying x + -0.75 = -5.706356105 Reorder the terms: -0.75 + x = -5.706356105 Solving -0.75 + x = -5.706356105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -5.706356105 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -5.706356105 + 0.75 x = -5.706356105 + 0.75 Combine like terms: -5.706356105 + 0.75 = -4.956356105 x = -4.956356105 Simplifying x = -4.956356105Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.456356105, -4.956356105}
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